The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  X  X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X^2+X X^2+X  0
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0
 0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0

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+72x^12+96x^13+340x^14+1120x^15+829x^16+1056x^17+488x^18+32x^19+56x^20+4x^22+2x^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 0.032 seconds.