The generator matrix

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

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+199x^12+634x^14+1214x^16+2040x^18+2046x^20+1252x^22+616x^24+168x^26+19x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=38, k=13 and d=12.
As d=12 is an upper bound for linear (38,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by an older version of Heurico in 0 seconds.