The generator matrix

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

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+91x^12+24x^13+108x^14+592x^15+97x^16+24x^17+72x^18+11x^20+4x^22

The gray image is a linear code over GF(2) with n=120, k=10 and d=48.
This code was found by Heurico 1.16 in 0.187 seconds.