The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+142x^10+487x^12+830x^14+1123x^16+954x^18+416x^20+122x^22+20x^24+1x^28

The gray image is a linear code over GF(2) with n=32, k=12 and d=10.
As d=10 is an upper bound for linear (32,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by an older version of Heurico in 0 seconds.