The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1 X^2  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X  1 X^2+X+1  1 X^2 X^2+X+1
 0  0  X X^2+X  0 X^2+X  X  X  X  0  0  X  X  X  X
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 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+68x^10+16x^11+340x^12+384x^13+868x^14+736x^15+885x^16+384x^17+332x^18+16x^19+52x^20+12x^22+2x^24

The gray image is a linear code over GF(2) with n=60, k=12 and d=20.
This code was found by Heurico 1.16 in 12.4 seconds.