The generator matrix
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 0 0 X X X
0 0 X 0 0 0 0 0 0 0 0 0 X X X 0
0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X
0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X
0 0 0 0 0 X 0 0 0 0 0 X X X X X
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X
0 0 0 0 0 0 0 X 0 0 0 X 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X
0 0 0 0 0 0 0 0 0 X 0 X X 0 0 X
0 0 0 0 0 0 0 0 0 0 X X X 0 X 0
generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+140x^8+448x^12+2918x^16+448x^20+140x^24+1x^32
The gray image is a linear code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 7.46 seconds.