The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+333x^64+352x^65+360x^66+176x^67+320x^68+160x^69+184x^70+48x^71+52x^72+32x^73+16x^74+4x^76+8x^80+2x^88

The gray image is a code over GF(2) with n=536, k=11 and d=256.
This code was found by Heurico 1.16 in 0.235 seconds.