The generator matrix

1 0 0 0 0 0 1 1 1 0 1 X 1 1 1 1 1 1 1
0 1 0 0 0 0 0 1 1 X 0 1 X X+1 X X+1 0 0 0
0 0 1 0 0 0 1 0 X 1 X+1 0 1 1 1 X 0 0 0
0 0 0 1 0 0 1 X X+1 X X+1 X+1 0 X 0 0 1 0 0
0 0 0 0 1 0 1 X+1 0 1 X 1 X+1 0 1 X X 1 0
0 0 0 0 0 1 X 1 X 1 X+1 1 X+1 X+1 0 X+1 0 X 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+14x^11+57x^12+130x^13+176x^14+206x^15+355x^16+378x^17+420x^18+554x^19+496x^20+430x^21+296x^22+234x^23+172x^24+78x^25+68x^26+16x^27+7x^28+8x^29

The gray image is a linear code over GF(2) with n=38, k=12 and d=11.
This code was found by Heurico 1.10 in 0.11 seconds.