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 2X  1  1  1  1  1  1  1  1 2X  1
 0  X  0 X+2  2 3X+2 2X+2  X  2 X+2 2X 3X 2X 3X+2 2X+2 3X  0 X+2 2X+2 3X 3X+2 2X  X  2 3X+2 2X+2 3X 2X  0 X+2  2  X  0 X+2  0 X+2  2  X  2  X  0  0 X+2 X+2  2  2 3X 3X  0 2X 2X  0 X+2 3X+2 X+2 3X+2 2X  2 2X+2 2X+2  2  X  X  X  X 2X  0
 0  0 2X+2  0  2  2  0  2 2X+2  0  2  0  0 2X+2  0 2X+2 2X 2X 2X 2X  2  2 2X+2 2X+2 2X  2 2X 2X+2 2X 2X+2 2X  2  0  0 2X+2 2X+2 2X+2 2X+2  0 2X  0  2  0 2X+2 2X+2 2X  2  0 2X 2X  2 2X+2 2X 2X  2  2  0  2  2 2X  0  2 2X+2 2X  0  0  0
 0  0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X  0 2X  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+103x^64+1088x^65+87x^66+512x^69+24x^72+192x^73+40x^74+1x^130

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 0.453 seconds.