The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  1  0  0  1  1
 0  1  0  1  0 X^2+X+1  1  1 X^2  X  1  1 X^2+X  X  0
 0  0  1  1  1  0  1  1  0 X^2+1 X^2 X+1  1 X+1 X^2+X
 0  0  0  X  0  0  0 X^2  X  X X^2  X  0 X^2+X X^2
 0  0  0  0  X X^2+X X^2+X  0 X^2  X X^2+X X^2+X  X  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+78x^10+190x^11+531x^12+964x^13+1454x^14+1780x^15+1409x^16+992x^17+543x^18+158x^19+75x^20+12x^21+4x^22+1x^26

The gray image is a linear code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 0.358 seconds.