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

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+160x^64+64x^66+64x^67+590x^68+384x^69+448x^70+64x^71+202x^72+58x^76+12x^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 2.47 seconds.