The generator matrix

 1  1  1  1  X  X  X  1  1  1  1  X  X  X  X  1  1  1
 0  X  0  X  0  X  X  0  0  X X^2+X X^2  X X^2+X  0  0  0  0
 0  0  X  X  X  X  0  0 X^2+X  X  0  X  X  0  0  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0
 0  0  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 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+93x^8+192x^10+32x^11+408x^12+224x^13+1052x^14+672x^15+2011x^16+1120x^17+4752x^18+1120x^19+2088x^20+672x^21+936x^22+224x^23+487x^24+32x^25+208x^26+32x^28+28x^30

The gray image is a linear code over GF(2) with n=72, k=14 and d=16.
This code was found by Heurico 1.16 in 0.668 seconds.