The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1  X  1  1  1
 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  0 X^3+X^2 X^2+X  0 X^3
 0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 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+15x^12+96x^13+286x^14+232x^15+294x^16+80x^17+8x^18+8x^19+1x^20+2x^22+1x^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 -3.24e-008 seconds.