The generator matrix

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

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+46x^10+116x^11+241x^12+496x^13+740x^14+842x^15+717x^16+472x^17+267x^18+112x^19+33x^20+8x^21+2x^22+2x^23+1x^26

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 0.089 seconds.