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 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 1 2 1 1 1 1 1 1 1 1 2X 1 1 1 1 2 1 2
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X+2 0 2X+2 0 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 0 2X+2 2X 2 0 2X+2 2X 2 0 2X+2 2 2X 2X+2 0 2 2X 0 2X 2X+2 2 2 2X+2 0 2X 0 2X 2X 2X 2X+2 2 2X+2 2X 0 2X+2 2 0 2X 0 2X 2X+2 2 2X 2 2X
0 0 2X 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 2X 2X 0 2X 0 2X 2X 0 0 0 2X 2X 2X 0 0 0
0 0 0 2X 0 0 0 2X 0 0 0 0 2X 0 0 2X 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 0 2X 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 0 2X 0
0 0 0 0 2X 0 0 0 2X 0 0 0 0 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 0 2X 0 0 0 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 0
0 0 0 0 0 2X 0 2X 0 0 2X 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 0 0 0 0 0 0 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 0 0 2X 0
0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 0 0 2X 2X 0 2X 0 0 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 2X 2X 2X 2X 0 0 0 2X 0 0 0 2X 2X 0 0 0 0 2X 0 0 0
generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+302x^64+256x^66+512x^67+64x^68+512x^69+256x^70+32x^72+64x^76+48x^80+1x^128
The gray image is a code over GF(2) with n=544, k=11 and d=256.
This code was found by Heurico 1.16 in 0.422 seconds.