The generator matrix

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

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+48x^13+86x^14+272x^15+63x^16+16x^17+9x^18+16x^19+1x^26

The gray image is a linear code over GF(2) with n=120, k=9 and d=52.
This code was found by Heurico 1.16 in -1.01e-007 seconds.