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 2X+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+2X+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 89.7 seconds.