The generator matrix

1 0 0 0 0 0 1 1 1 0 1 0 X 0 1 0 1 X 1 1 1
0 1 0 0 0 0 0 0 1 0 X+1 1 X 1 X 1 X 0 X X+1 0
0 0 1 0 0 0 0 1 0 X 1 1 1 X X+1 0 X 0 X+1 1 0
0 0 0 1 0 0 0 1 1 1 1 X 0 X+1 1 X+1 X+1 1 X 1 1
0 0 0 0 1 0 1 0 X+1 1 X+1 X+1 1 1 1 0 1 1 0 X 0
0 0 0 0 0 1 1 X+1 X 1 1 0 X+1 1 1 X 0 1 X+1 1 0
0 0 0 0 0 0 X X 0 X X 0 X 0 0 X X 0 0 0 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+44x^13+126x^14+240x^15+321x^16+444x^17+659x^18+800x^19+933x^20+966x^21+935x^22+916x^23+707x^24+466x^25+305x^26+152x^27+79x^28+62x^29+23x^30+4x^31+7x^32+2x^33

The gray image is a linear code over GF(2) with n=42, k=13 and d=13.
This code was found by Heurico 1.10 in 0.469 seconds.