The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  X  X
 0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  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  0 X^2
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 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+105x^8+408x^12+384x^14+2048x^15+819x^16+128x^18+168x^20+35x^24

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 0.0471 seconds.