The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X  1  1 X^2
 0  1 X+1 X^2+X X^3+X^2+1  1 X^2+X+1 X^3  1 X^3+X X^2+1  1 X+1 X^3+X^2+X+1 X^3
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3  0 X^3  0 X^3 X^2
 0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  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+202x^12+384x^13+960x^14+1024x^15+951x^16+384x^17+160x^18+30x^20

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 0.046 seconds.