The generator matrix

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

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+95x^12+128x^13+672x^14+256x^15+687x^16+128x^17+64x^18+16x^20+1x^28

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 0.094 seconds.