The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+139x^12+64x^13+250x^14+128x^15+254x^16+64x^17+100x^18+21x^20+2x^22+1x^24

The gray image is a linear code over GF(2) with n=60, k=10 and d=24.
This code was found by Heurico 1.16 in 0.0126 seconds.