The generator matrix

 1  1  1  1  X  X  X  1  1  0  1  1  X  X  X
 0  X  0  X  0  X  X  0  0  0  X X^2+X  X X^2+X  0
 0  0  X  X  X  X  0  0 X^2+X  X  X  0  X  0  0
 0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2
 0  0  0  0  0  0  0  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 8.

Homogenous weight enumerator: w(x)=1x^0+161x^8+456x^10+2288x^12+5160x^14+5595x^16+2008x^18+624x^20+56x^22+35x^24

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 5.15 seconds.