The generator matrix

 1  1  1  1  1  1  1  1  1  X  0  X  1  X  1
 0  X  0  X  0  0  X X^2+X X^2 X^2 X^2  0 X^2  0  X
 0  0  X  X  0 X^2+X  X X^2  0  X  X X^2+X  X  0  X
 0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  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+20x^10+32x^11+51x^12+132x^13+182x^14+192x^15+190x^16+120x^17+48x^18+32x^19+13x^20+4x^21+6x^22+1x^24

The gray image is a linear code over GF(2) with n=60, k=10 and d=20.
This code was found by Heurico 1.16 in 0.0086 seconds.