The generator matrix

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

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+42x^10+76x^11+115x^12+244x^13+351x^14+376x^15+366x^16+264x^17+109x^18+60x^19+29x^20+4x^21+9x^22+1x^24+1x^26

The gray image is a linear code over GF(2) with n=60, k=11 and d=20.
This code was found by Heurico 1.16 in 0.0295 seconds.