The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  X  X  0  X
 0  X  0  X X^3  0 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^2+X X^3+X^2+X X^2 X^3 X^2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  0 X^3 X^3+X^2  X  X X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  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+156x^12+112x^13+482x^14+544x^15+499x^16+112x^17+124x^18+16x^20+2x^22

The gray image is a linear code over GF(2) with n=120, k=11 and d=48.
This code was found by Heurico 1.16 in 0.016 seconds.