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

generates a code of length 68 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+12x^65+51x^66+116x^67+662x^68+116x^69+52x^70+12x^71+1x^72+1x^130

The gray image is a code over GF(2) with n=544, k=10 and d=260.
This code was found by Heurico 1.16 in 76.2 seconds.