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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+8x^65+60x^66+112x^67+62x^68+8x^69+1x^72+1x^78+2x^82+1x^86

The gray image is a code over GF(2) with n=536, k=8 and d=260.
This code was found by Heurico 1.16 in 0.282 seconds.