The generator matrix

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

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+154x^10+64x^11+662x^12+640x^13+1743x^14+1664x^15+1743x^16+640x^17+662x^18+64x^19+154x^20+1x^30

The gray image is a linear code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 3.63 seconds.