The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  1  1  1
 0  X  0  0  0  0  0  0  0  X X^2 X^2+X X^2+X X^2 X^2
 0  0  X  0  0  0  X X^2+X  X  X X^2  0 X^2+X  0  0
 0  0  0  X  0  X  X X^2+X  0  0  X  X X^2+X  X  0
 0  0  0  0  X  X  0 X^2+X  X  0 X^2+X X^2+X X^2  0  X
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+91x^8+106x^9+218x^10+366x^11+672x^12+1434x^13+3152x^14+4366x^15+3055x^16+1454x^17+660x^18+378x^19+272x^20+78x^21+64x^22+10x^23+5x^24+2x^26

The gray image is a linear code over GF(2) with n=60, k=14 and d=16.
This code was found by Heurico 1.16 in 0.794 seconds.