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.