The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+70x^9+308x^10+784x^11+1962x^12+3574x^13+6450x^14+6516x^15+6369x^16+3554x^17+2056x^18+792x^19+242x^20+66x^21+18x^22+4x^23+2x^24

The gray image is a linear code over GF(2) with n=60, k=15 and d=18.
This code was found by Heurico 1.16 in 3.41 seconds.