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

generates a code of length 68 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+60x^67+175x^68+15x^72+1x^76+4x^83

The gray image is a code over GF(2) with n=544, k=8 and d=268.
This code was found by Heurico 1.16 in 37.8 seconds.