The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  1  1 X^2
 0  X  0  0  0  X X^2+X  X  X X^2 X^2+X X^2+X  X  X  X
 0  0  X  0  X  X X^2+X  0  X  0 X^2 X^2+X X^2+X  X  0
 0  0  0  X  X  0 X^2+X  X  0  X  0  X  X X^2  X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 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+161x^10+32x^11+388x^12+256x^13+972x^14+448x^15+1013x^16+256x^17+390x^18+32x^19+132x^20+12x^22+2x^24+1x^26

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 22.8 seconds.