The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+157x^10+8x^11+464x^12+224x^13+900x^14+560x^15+941x^16+224x^17+466x^18+8x^19+128x^20+12x^22+2x^24+1x^26

The gray image is a linear code over GF(2) with n=60, k=12 and d=20.
This code was found by Heurico 1.16 in 1.85 seconds.