The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^2  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 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+18x^12+36x^13+13x^14+376x^15+13x^16+36x^17+18x^18+1x^30

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.