The generator matrix

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

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+312x^10+824x^11+2239x^12+3616x^13+6002x^14+6416x^15+6462x^16+3808x^17+2084x^18+632x^19+289x^20+64x^21+18x^22+1x^24

The gray image is a linear code over GF(2) with n=60, k=15 and d=20.
This code was found by Heurico 1.13 in 1.5 seconds.