The generator matrix

 1  1  1  1  1  1  X  1  1  0  X  X  X  X  X
 0  X  0 X^2+X  0 X^2+X  X X^2 X^2+X  X X^2+X X^2+X  0  0  0
 0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  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+39x^10+134x^12+346x^14+335x^16+120x^18+42x^20+6x^22+1x^26

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 0.00863 seconds.