The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1  0  0  0  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X+1  1  1  1  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  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 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 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+55x^8+86x^10+128x^11+736x^12+384x^13+2184x^14+1024x^15+2199x^16+384x^17+756x^18+128x^19+80x^20+40x^22+1x^24+6x^26

The gray image is a linear code over GF(2) with n=60, k=13 and d=16.
This code was found by Heurico 1.16 in 0.125 seconds.