The generator matrix

 1  0  0  1  1  1  X  1  1 X^2  1  1 X^2  1  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X^2+1  1  X X^2+X  X X+1 X+1
 0  0  1  1 X^2+X+1 X^2+X  1  X X+1  X  1  0  1 X+1  0
 0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  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+84x^10+160x^11+580x^12+960x^13+1380x^14+1856x^15+1397x^16+960x^17+572x^18+160x^19+68x^20+12x^22+2x^24

The gray image is a linear code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 0.319 seconds.