The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^3+X^2 X^3+X  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X X^3+X^2+X+1 X^3+1  1  1  0 X^2+X X^3
 0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  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+32x^13+190x^14+64x^15+191x^16+32x^17+2x^22

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 6.87e-008 seconds.