The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  X  1  1  X  X  1  1
 0  1  0  0  0  0  0  0 X+1  0 X+1  1  X  1  X  1  X  0  X  1  0
 0  0  1  0  0  0  0 X+1  1  1  1  X X+1  0  0  X  1  1  1 X+1  0
 0  0  0  1  0  0  0  1  0  X  1  1 X+1  X  1  0  X  0 X+1 X+1  X
 0  0  0  0  1  0  1  0  1  1  X  0  1  X  1 X+1 X+1 X+1  X  1  X
 0  0  0  0  0  1  1 X+1  X X+1  0  1  0  1  0  0  X X+1  X  0  0
 0  0  0  0  0  0  X  X  0  X  0  X  0  0  X  X  X  0  X  X  X

generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+38x^13+161x^14+212x^15+299x^16+472x^17+638x^18+776x^19+964x^20+1028x^21+894x^22+896x^23+694x^24+472x^25+328x^26+152x^27+84x^28+38x^29+25x^30+12x^31+6x^32+2x^34

The gray image is a linear code over GF(2) with n=42, k=13 and d=13.
This code was found by Heurico 1.16 in 1.38 seconds.