The generator matrix

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

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+148x^8+140x^9+351x^10+356x^11+592x^12+908x^13+3008x^14+5380x^15+2985x^16+900x^17+614x^18+396x^19+360x^20+100x^21+120x^22+12x^23+10x^24+3x^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 1.05 seconds.