The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X^2 1 1 1 X X^2 1 1 X 1 0 1 X
0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X X^2 X X^2 0 0 X^2 X 0 X^2+X X X^2 0 0 X^2+X
0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X X X X^2 0 X X^2+X X^2+X 0 X X X X^2+X 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2
0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2
0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2
generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.
Homogenous weight enumerator: w(x)=1x^0+60x^23+76x^24+76x^25+161x^26+264x^27+281x^28+236x^29+292x^30+256x^31+135x^32+68x^33+54x^34+56x^35+14x^36+4x^37+4x^38+4x^39+4x^40+1x^42+1x^44
The gray image is a linear code over GF(2) with n=116, k=11 and d=46.
This code was found by Heurico 1.16 in 21.2 seconds.