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 X 1 1 1 1 1 1 X 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 1 X 1 1 X
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 0 2X 0 0 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 0 0 2X 2X
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 0 2X 0 0 0 2X 0 2X 0 0 0 2X 2X 2X 2X
0 0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 0 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X
0 0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 0 2X 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 0 0 2X 2X 2X 2X
0 0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 2X 0 0 2X 0 2X 0 0 2X 0 0 2X 0 0 0 0 2X 0 2X 0 0 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 0 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 2X 0 2X 2X 0 2X 2X 2X 2X
0 0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 0 0 0 0 0 2X 0 0 2X 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 0 0 2X
generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+150x^64+448x^68+1024x^69+256x^70+112x^72+56x^80+1x^128
The gray image is a code over GF(2) with n=552, k=11 and d=256.
This code was found by Heurico 1.16 in 88.3 seconds.