The generator matrix

 1  1  1  1  X  1  1  0  X  1  1  X  X  X  1
 0  X  0 X^2+X  X  0 X^2+X  X  X  0 X^2+X X^2+X  0  0  0
 0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  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  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  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 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  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+63x^8+16x^9+62x^10+96x^11+312x^12+240x^13+1088x^14+320x^15+1103x^16+240x^17+332x^18+96x^19+56x^20+16x^21+48x^22+1x^24+6x^26

The gray image is a linear code over GF(2) with n=60, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0422 seconds.