The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+36x^8+98x^9+143x^10+224x^11+354x^12+798x^13+1507x^14+1836x^15+1522x^16+830x^17+365x^18+232x^19+129x^20+66x^21+33x^22+12x^23+5x^24+1x^28

The gray image is a linear code over GF(2) with n=60, k=13 and d=16.
This code was found by Heurico 1.16 in 0.285 seconds.