The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+34x^11+92x^12+188x^13+327x^14+468x^15+602x^16+796x^17+1011x^18+1082x^19+1041x^20+856x^21+633x^22+490x^23+297x^24+140x^25+73x^26+36x^27+15x^28+4x^29+4x^30+2x^31

The gray image is a linear code over GF(2) with n=38, k=13 and d=11.
This code was found by Heurico 1.10 in 0.36 seconds.