The generator matrix

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

generates a code of length 22 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+12x^13+52x^14+106x^15+262x^16+322x^17+490x^18+690x^19+714x^20+906x^21+970x^22+950x^23+858x^24+694x^25+486x^26+278x^27+206x^28+114x^29+42x^30+24x^31+7x^32+8x^34

The gray image is a linear code over GF(2) with n=44, k=13 and d=13.
This code was found by an older version of Heurico in 0 seconds.