The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+296x^9+1126x^10+2988x^11+8397x^12+14608x^13+25221x^14+25588x^15+25426x^16+14760x^17+8373x^18+2900x^19+1055x^20+288x^21+31x^22+12x^23+1x^24+1x^26

The gray image is a linear code over GF(2) with n=60, k=17 and d=18.
This code was found by Heurico 1.13 in 18.8 seconds.