The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 1 0 1 1 0 1 X 1 1 1 1 0 0 1 1 1 1 0 1 0 1 X 1 1 X 1 1 1 1 0 X 1 X 1 1 0 0 1 1 1 1 0 X 0 1 X 1 X X 0
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 X+1 0 1 0 X+1 1 X+1 1 0 X+1 X+1 0 1 1 X 0 X+1 X 1 1 1 0 1 0 X 1 X+1 1 1 1 1 1 1 1 0 X 1 1 X+1 X X+1 X+1 1 1 1 X 1 1 X 0 1
0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X X X X X X 0 X X 0 X X X X 0 X 0 0 X X X 0 0 X X 0 X 0 0 X X X X X X 0 0 0 X X 0 X X 0 X 0 0 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 X X X X 0 X X X X X X X X 0 X X 0 X X 0 X 0 X 0 X X 0 0 0 X 0 0 X X 0 0 0 X X X X 0 0 0
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 X 0 0 0 X X 0 X 0 X X 0 X 0 X 0 X 0 0 X X 0 0 X X X X X X 0 X 0 0 X 0 0 0 X X 0 0 0 0 X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X X X X 0 0 X X X 0 X X 0 0 0 0 X X 0 X 0 0 0 X X 0 0 0 X 0 0 X X 0 X X 0 X X 0 0 0 X 0 X 0 0 X X
0 0 0 0 0 0 X 0 0 X 0 0 X X 0 X X 0 X X X X X X X 0 0 X X X 0 X X 0 X X 0 X 0 0 X X 0 X X X 0 X 0 X 0 0 X 0 0 0 0 0 X X 0 X X X 0 X
0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X X 0 0 X 0 0 0 X X 0 X X X 0 X X 0 X X 0 X X 0 X 0 X 0 X 0 X 0 0 0 0 X 0 0 X X 0 0 X X 0 0 0 X X 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X X X 0 0 0 X X 0 X 0 0 X X 0 0 X 0 X 0 X X X X X X 0 0 0 0 0 X X X X X 0 X X X X 0 0 X X X 0 0 X X 0
generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+45x^56+38x^57+106x^58+78x^59+121x^60+110x^61+88x^62+148x^63+118x^64+144x^65+122x^66+144x^67+113x^68+128x^69+93x^70+108x^71+65x^72+90x^73+63x^74+34x^75+31x^76+2x^77+22x^78+9x^80+12x^82+7x^84+5x^86+2x^88+1x^90
The gray image is a linear code over GF(2) with n=132, k=11 and d=56.
This code was found by Heurico 1.16 in 0.757 seconds.