The generator matrix

 1  1  1  1  1  1  1  X X^3  1  X  X  X  X  X
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X  X X^3+X^2+X X^2+X X^3+X^2+X X^2 X^3 X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^3+X^2 X^2 X^2  0 X^3 X^2 X^3+X^2 X^3
 0  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  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+193x^12+64x^13+568x^14+384x^15+610x^16+64x^17+136x^18+27x^20+1x^24

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 0.031 seconds.