The generator matrix

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

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+89x^12+150x^13+207x^14+168x^15+187x^16+112x^17+80x^18+16x^19+11x^20+2x^21+1x^22

The gray image is a linear code over GF(2) with n=60, k=10 and d=24.
This code was found by Heurico 1.11 in 0.016 seconds.