The generator matrix

 1  1  1  1  1  1  1  X  X  1  1 X^2  1  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2 X^3+X^2+X X^3+X X^3  X X^3+X X^2+X X^2
 0  0  X  X X^2 X^2+X  X  X X^3 X^2 X^2+X X^3+X X^2 X^2+X X^3+X^2
 0  0  0 X^2  0 X^3 X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^2 X^3 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+317x^12+96x^13+1080x^14+1088x^15+1146x^16+96x^17+232x^18+39x^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 13.9 seconds.