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  1  1  1  1 2X  1  1 2X  1 2X  1
 0  X  0  X 2X 2X 3X 3X  2 X+2  2 X+2 2X+2 3X+2 2X+2 3X+2  0  X 2X X+2  2 X+2  X  0  2 3X+2 2X 3X  2  2 X+2 3X X+2 2X X+2 2X+2  2  X  X 2X 2X+2 3X+2 2X+2  X 2X+2 X+2  0 3X+2 2X+2  X 3X+2  0  2  X 2X+2 2X 2X 3X+2  X 3X  0  0  0 2X 3X+2 2X 3X
 0  0  X  X  2 3X+2 X+2 2X+2  2 X+2  X  0  0  X 3X+2 2X+2  0  X 3X+2 2X+2 X+2 2X 3X+2  2 2X+2 X+2 3X  2  X  0 3X  0 2X+2 2X 3X+2 X+2 2X+2 2X 3X 3X X+2  0  X X+2 2X  X X+2 2X+2 2X 3X 2X 2X+2 3X  2 2X+2  2 2X 3X+2 2X+2 2X 2X X+2  X  0  X 2X X+2
 0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0 2X 2X  0  0 2X  0  0  0  0 2X  0 2X  0  0

generates a code of length 67 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+526x^64+768x^66+224x^68+256x^70+272x^72+1x^128

The gray image is a code over GF(2) with n=536, k=11 and d=256.
This code was found by Heurico 1.16 in 22.2 seconds.