The generator matrix

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

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+109x^8+16x^9+452x^10+416x^11+1292x^12+1776x^13+2244x^14+3776x^15+2223x^16+1776x^17+1324x^18+416x^19+452x^20+16x^21+76x^22+19x^24

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 0.691 seconds.