The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 1 1 X X 1 X X X X X 1 1 1 1 1 1 1 1 1 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 0 0 2X
0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 0 0 0 2X 2X 2X 2X
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 0 0 0
generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+65x^66+160x^67+10x^68+10x^70+5x^72+1x^74+4x^82
The gray image is a code over GF(2) with n=536, k=8 and d=264.
This code was found by Heurico 1.16 in 1.16 seconds.