The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 0 0 1 0 1 1 0
0 0 X 0 0 0 0 0 0 0 X 0 X X X 0 X 0 0 0 X
0 0 0 X 0 0 0 0 0 X 0 0 X 0 X X X 0 0 X X
0 0 0 0 X 0 0 0 0 0 X X 0 X 0 X 0 X 0 0 X
0 0 0 0 0 X 0 0 0 0 0 X X X X 0 0 X X 0 0
0 0 0 0 0 0 X 0 0 X 0 X X X 0 0 0 0 0 X X
0 0 0 0 0 0 0 X 0 0 X X X 0 X X X X X X X
0 0 0 0 0 0 0 0 X 0 0 0 X X 0 X X X 0 X 0
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+59x^14+165x^16+333x^18+421x^20+518x^22+390x^24+98x^26+42x^28+15x^30+4x^32+1x^34+1x^36
The gray image is a linear code over GF(2) with n=42, k=11 and d=14.
This code was found by Heurico 1.16 in 33.3 seconds.