The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X X^2+X X^2+X  X X^2
 0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2+X  X  0  0
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  0 X^2+X  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  0 X^2+X X^2  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+38x^10+80x^11+98x^12+96x^13+119x^14+1184x^15+119x^16+96x^17+98x^18+80x^19+38x^20+1x^30

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 0.0323 seconds.