The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  0  X  0

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+68x^12+34x^14+85x^16+68x^18+512x^19+68x^20+85x^22+34x^24+68x^26+1x^38

The gray image is a linear code over GF(2) with n=38, k=10 and d=12.
This code was found by Heurico 1.16 in 0.023 seconds.