The generator matrix

 1  0  1  1  1 X^3+X^2  1  1  X  1  1  1  X  1  1
 0  1  1 X^2 X^3+X+1  1 X^3+X X^3+1  1 X^3+X^2+X  0  X X^3  X X^3
 0  0  X X^3+X X^2 X^2+X X^2+X X^3 X^3+X X^3+X^2 X^3+X^2  0 X^3+X^2+X X^2 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+33x^12+244x^13+430x^14+708x^15+338x^16+222x^17+55x^18+8x^19+4x^20+2x^21+3x^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 0.078 seconds.