The generator matrix
1 1 1 1 1 1 1 1 X X X^3+X^2 X 1 1 1 1
0 X 0 X X^3 0 X^2+X X^3+X^2+X X^2 X X X^3+X^2 X^3+X^2 X^2+X X^2 0
0 0 X X 0 X^3+X^2+X X^2+X X^3 X X^2+X X^2 X^3+X^2+X X^2 X^3+X X^3+X^2+X 0
0 0 0 X^2 X^3+X^2 X^2 X^3 X^2 0 X^2 X^2 X^2 X^2 X^2 X^3 X^3
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+49x^12+212x^13+310x^14+864x^15+1222x^16+912x^17+272x^18+176x^19+55x^20+12x^21+10x^22+1x^24
The gray image is a linear code over GF(2) with n=128, k=12 and d=48.
This code was found by Heurico 1.16 in 0.047 seconds.