The generator matrix

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

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+88x^11+228x^12+356x^13+553x^14+868x^15+1260x^16+1658x^17+2089x^18+2240x^19+1987x^20+1670x^21+1283x^22+884x^23+591x^24+342x^25+171x^26+80x^27+29x^28+6x^29

The gray image is a linear code over GF(2) with n=38, k=14 and d=11.
This code was found by Heurico 1.10 in 1.33 seconds.