The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  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+35x^12+32x^13+32x^14+320x^15+30x^16+32x^17+16x^18+13x^20+1x^24

The gray image is a linear code over GF(2) with n=120, k=9 and d=48.
This code was found by Heurico 1.16 in 6.87e-008 seconds.