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  1  X  1  1  1  1  1  1  1  1  1  1  X  1 2X+2 2X+2  1  X
 0  2  0  0  0 2X+2  2 2X+2  0  0 2X 2X 2X+2 2X+2 2X+2  2  2  0 2X  2  2  2 2X  0 2X+2  0 2X  0 2X+2 2X 2X+2 2X+2 2X+2 2X+2 2X 2X  0 2X  2  0 2X 2X+2  2  0  0  2 2X+2 2X+2 2X  0 2X+2  0  2  2 2X+2  0 2X 2X  2  2 2X+2 2X+2  2  2 2X  2  2  0 2X
 0  0  2  0 2X+2 2X+2  2  0 2X+2  0  0 2X+2 2X+2 2X+2 2X 2X 2X+2 2X  2 2X 2X+2  0  2  0  0 2X  0 2X+2 2X+2  2 2X  2  2 2X+2 2X+2  2  0 2X 2X  0 2X  0  0  2 2X+2 2X+2  2 2X  0 2X+2  2 2X 2X+2  0 2X 2X  2  0 2X+2 2X  0 2X 2X  0 2X+2 2X 2X+2 2X+2 2X
 0  0  0  2 2X+2  0  2 2X+2 2X+2  0 2X+2 2X 2X  2  2  0  0  2 2X  2 2X+2 2X 2X+2 2X 2X 2X  2  0 2X  2  2 2X+2  2  2  0  0  2  0  0 2X+2  0  2 2X+2 2X+2  2 2X 2X  0 2X+2  2  0  2  2 2X  0  0 2X+2 2X 2X 2X+2  0 2X+2 2X 2X  0  0  2  0 2X
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X  0  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X  0  0  0  0 2X  0  0  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X 2X  0

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+154x^64+48x^66+192x^67+328x^68+640x^69+288x^70+192x^71+96x^72+48x^74+56x^76+4x^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 0.734 seconds.