The generator matrix

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

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+123x^12+160x^13+322x^14+832x^15+342x^16+160x^17+92x^18+13x^20+2x^22+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 0.141 seconds.