The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+56x^11+72x^12+168x^13+50x^14+320x^15+91x^16+176x^17+12x^18+40x^19+28x^20+8x^21+2x^22

The gray image is a linear code over GF(2) with n=60, k=10 and d=22.
This code was found by Heurico 1.16 in 3.02 seconds.