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  2  1  1  1  1  1  1  1  1 2X  1  1  1  1  2  1  2
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X+2  0 2X+2  0  0 2X+2  0 2X+2  0 2X+2 2X  2 2X  2  0 2X+2 2X  2  0 2X+2 2X  2  0 2X+2  2 2X 2X+2  0  2 2X  0 2X 2X+2  2  2 2X+2  0 2X  0 2X 2X 2X 2X+2  2 2X+2 2X  0 2X+2  2  0 2X  0 2X 2X+2  2 2X  2 2X
 0  0 2X  0  0  0  0  0  0  0  0 2X  0 2X 2X  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0  0
 0  0  0 2X  0  0  0 2X  0  0  0  0 2X  0  0 2X  0  0  0  0  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0
 0  0  0  0 2X  0  0  0 2X  0  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0 2X  0  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0 2X  0
 0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0  0  0 2X  0
 0  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X  0  0  0 2X 2X  0  0  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+302x^64+256x^66+512x^67+64x^68+512x^69+256x^70+32x^72+64x^76+48x^80+1x^128

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 0.422 seconds.