The generator matrix

 1  0  1  1  1  0  X  1  1 X^2+X  1  1 X^2  X  1
 0  1  1  0 X+1  1  X  X X^2+X+1  1 X^2+X X+1  1 X^2  0
 0  0  X X^2+X  0 X^2+X  X  X X^2+X  0  0 X^2  X  X  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0
 0  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 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 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+71x^8+16x^9+214x^10+672x^11+960x^12+1776x^13+2840x^14+3264x^15+2855x^16+1776x^17+980x^18+672x^19+208x^20+16x^21+56x^22+1x^24+6x^26

The gray image is a linear code over GF(2) with n=60, k=14 and d=16.
This code was found by Heurico 1.16 in 0.486 seconds.