The generator matrix
1 1 1 1 1 1 1 1 X X X X 1 1 X^2 X^2 0 X^3
0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 0 X^3 0 X^3 X^3+X^2 X^2 X^2 X^2
generates a code of length 18 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+58x^18+2x^20+2x^22+1x^24
The gray image is a linear code over GF(2) with n=144, k=6 and d=72.
As d=72 is an upper bound for linear (144,6,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 6.
This code was found by Heurico 1.16 in -6.48e-008 seconds.