The generator matrix

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

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+321x^12+1368x^14+768x^15+1314x^16+296x^18+27x^20+1x^24

The gray image is a linear code over GF(2) with n=120, k=12 and d=48.
This code was found by Heurico 1.16 in 1.48 seconds.