The generator matrix

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

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+218x^12+352x^13+940x^14+1088x^15+943x^16+352x^17+176x^18+22x^20+4x^22

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 0.032 seconds.