The generator matrix

 1  1  1  1  1  1  1  1  1  X  1 X^2  X  1  1
 0 X^3+X^2  0 X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^2 X^3  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3
 0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 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+68x^12+32x^13+258x^14+320x^15+253x^16+32x^17+44x^18+12x^20+2x^22+2x^24

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 0.829 seconds.