The generator matrix

 1  1  1  1  X  X  X  1  1  1  1  X  X  X  1
 0  X  0  X  0  X  X  0 X^2  X X^2+X  X  X  0  0
 0  0  X  X  X  X  0  0  X  X  0  X  X X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  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+34x^8+20x^9+93x^10+168x^11+160x^12+620x^13+224x^14+1456x^15+221x^16+620x^17+170x^18+168x^19+88x^20+20x^21+24x^22+8x^24+1x^26

The gray image is a linear code over GF(2) with n=60, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0456 seconds.