The generator matrix

 1  0  1  1  1  0  1  1  X  1  1 X^2  1  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2 X^2+X+1  1 X^2+1 X^2+X+1  0
 0  0  X X^2+X  0 X^2+X  X  X X^2+X X^2+X  X  X  0  X  0
 0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  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+22x^10+44x^11+76x^12+348x^13+288x^14+496x^15+283x^16+352x^17+70x^18+36x^19+24x^20+4x^21+4x^22

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 0.021 seconds.