The generator matrix
1 0 0 0 1 1 1 0 1 1 1 X 1 X X 1 1 X 1 1 X
0 1 0 0 0 1 1 1 0 0 1 1 X+1 1 X 0 1 1 0 0 0
0 0 1 0 1 1 0 1 0 1 1 0 0 X+1 1 0 0 0 X 0 X
0 0 0 1 1 0 1 1 1 0 1 1 X 0 1 0 1 X+1 X 0 0
0 0 0 0 X 0 0 0 0 0 0 X 0 X 0 X X X 0 X X
0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X X X X
0 0 0 0 0 0 0 X 0 0 0 0 X 0 X X 0 0 X 0 X
0 0 0 0 0 0 0 0 X 0 0 0 X X X 0 X X 0 X X
0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 X 0 0 X 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 X X 0 0
generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+310x^12+672x^14+2970x^16+4032x^18+9606x^20+5376x^22+6552x^24+2112x^26+962x^28+96x^30+77x^32+2x^36
The gray image is a linear code over GF(2) with n=42, k=15 and d=12.
This code was found by Heurico 1.16 in 10.4 seconds.