The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+39x^6+141x^8+312x^10+1640x^12+4011x^14+4096x^15+4011x^16+1640x^18+312x^20+141x^22+39x^24+1x^30

The gray image is a linear code over GF(2) with n=60, k=14 and d=12.
This code was found by Heurico 1.16 in 74 seconds.