The generator matrix
1 1 1 1 1 1 1 X X 1 1 X^2 1 1 1
0 X 0 X X^3 0 X^2+X X^3+X^2 X^3+X^2+X X^3+X X^3 X X^3+X X^2+X X^2
0 0 X X X^2 X^2+X X X X^3 X^2 X^2+X X^3+X X^2 X^2+X X^3+X^2
0 0 0 X^2 0 X^3 X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^2 X^3 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+317x^12+96x^13+1080x^14+1088x^15+1146x^16+96x^17+232x^18+39x^20+1x^24
The gray image is a linear code over GF(2) with n=120, k=12 and d=48.
This code was found by Heurico 1.16 in 13.9 seconds.