The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  X  1
 0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  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  0  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 X^2  0 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  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+55x^8+22x^10+96x^12+128x^13+72x^14+1280x^15+87x^16+128x^17+116x^18+16x^20+40x^22+1x^24+6x^26

The gray image is a linear code over GF(2) with n=60, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0138 seconds.