The generator matrix
1 1 1 1 1 1 1 1 X X X 1 X^2 X^2 X^2 X 1 1
0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3
0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3
generates a code of length 18 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.
Homogenous weight enumerator: w(x)=1x^0+12x^17+35x^18+8x^19+3x^20+4x^21+1x^22
The gray image is a linear code over GF(2) with n=144, k=6 and d=68.
This code was found by Heurico 1.16 in 0 seconds.