The generator matrix
1 0 0 0 0 1 1 1 X 1 1 1 1 1 0 X 1 1 0 1 X
0 1 0 0 0 0 0 0 1 0 1 1 X+1 X 1 0 1 1 X X+1 1
0 0 1 0 0 0 0 0 1 1 X+1 X 0 1 X X 1 0 1 X X+1
0 0 0 1 0 0 1 1 1 X+1 X 1 1 X+1 1 1 0 0 0 X 0
0 0 0 0 1 1 1 0 1 X 1 0 X+1 X+1 X+1 X+1 X X 1 1 X+1
0 0 0 0 0 X 0 0 0 0 0 0 X X X X 0 X 0 X 0
0 0 0 0 0 0 X 0 0 0 0 X X X 0 X X 0 0 X X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X X
generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+242x^14+737x^16+1209x^18+1796x^20+2024x^22+1362x^24+574x^26+196x^28+46x^30+4x^32+1x^34
The gray image is a linear code over GF(2) with n=42, k=13 and d=14.
As d=14 is an upper bound for linear (42,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.16 in 2.69 seconds.