The generator matrix
1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1
0 X^3+X^2 0 0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2 0 X^3 X^3 X^2 X^3 0
0 0 X^3+X^2 0 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 0 X^2 0 0 X^3
0 0 0 X^3+X^2 X^2 X^3 X^2 X^2 0 X^3 X^3 X^2 0 X^2 X^3+X^2 X^2
generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+17x^12+32x^13+69x^14+32x^15+729x^16+32x^17+62x^18+32x^19+10x^20+5x^22+2x^24+1x^28
The gray image is a linear code over GF(2) with n=128, k=10 and d=48.
This code was found by Heurico 1.16 in 1.05e-007 seconds.