The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+48x^10+122x^11+307x^12+432x^13+781x^14+700x^15+833x^16+408x^17+282x^18+122x^19+43x^20+8x^21+9x^22

The gray image is a linear code over GF(2) with n=60, k=12 and d=20.
This code was found by Heurico 1.16 in 0.0755 seconds.