The generator matrix
1 0 0 1 1 1 X 1 0 1 1 1 1 1 0 X
0 1 0 0 1 X+1 1 X X 0 X+1 1 1 X+1 1 1
0 0 1 1 X+1 0 X+1 1 1 X X+1 0 1 X+1 1 X
0 0 0 X X X 0 0 X 0 0 0 X X 0 X
generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+58x^14+27x^16+28x^18+4x^20+10x^22
The gray image is a linear code over GF(2) with n=32, k=7 and d=14.
As d=14 is an upper bound for linear (32,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00967 seconds.