The generator matrix

 1  0  0  1  1  1 X^2+X  1  X  X  1 X^2 X^2  1  1
 0  1  0  1  0  1  1  0  1  1 X^2+X  0 X^2  0  0
 0  0  1  1  1  0  1  0 X+1  1  1  0  1 X^2  0
 0  0  0  X  0  0  X X^2+X X^2 X^2  0  X  0 X^2  0
 0  0  0  0  X  0  X X^2+X  0  X X^2 X^2  0  0  0
 0  0  0  0  0  X  X X^2  X X^2+X  X X^2+X  0  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+103x^8+88x^9+598x^10+736x^11+2027x^12+3688x^13+5526x^14+7360x^15+5277x^16+3688x^17+2226x^18+736x^19+516x^20+88x^21+98x^22+11x^24+1x^28

The gray image is a linear code over GF(2) with n=60, k=15 and d=16.
This code was found by Heurico 1.16 in 2.73 seconds.