The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  X  X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+1 X^2+X  1  0  0  0
 0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0
 0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  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+19x^10+22x^11+51x^12+194x^13+65x^14+340x^15+54x^16+188x^17+37x^18+22x^19+21x^20+2x^21+7x^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 0.00619 seconds.