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.