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

generates a code of length 68 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+103x^64+1088x^66+87x^68+512x^70+24x^72+192x^74+40x^76+1x^132

The gray image is a code over GF(2) with n=544, k=11 and d=256.
This code was found by Heurico 1.16 in 0.39 seconds.