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  X X+1  X  1  1  0  X  1  1  X  X X+1
 0  0  1  0  0  0  0  0  1 X+1  X  1  X  1  0  1  X  X  0
 0  0  0  1  0  0  0  0  0  0  0  1 X+1  1  X  1  1  X X+1
 0  0  0  0  1  0  0  1  0 X+1  X  X  1 X+1  0  X  1  X  1
 0  0  0  0  0  1  0  1  X  X  1 X+1  0 X+1  0  0  1 X+1  X
 0  0  0  0  0  0  1  1 X+1  0  1  0  X  1  1  X  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+68x^11+228x^12+416x^13+553x^14+814x^15+1260x^16+1692x^17+2089x^18+2170x^19+1987x^20+1720x^21+1283x^22+914x^23+591x^24+316x^25+171x^26+66x^27+29x^28+16x^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 1.16 in 8.53 seconds.