The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+293x^64+552x^65+610x^66+572x^67+419x^68+508x^69+408x^70+232x^71+210x^72+144x^73+54x^74+28x^75+38x^76+12x^77+8x^78+5x^80+1x^84+1x^88

The gray image is a code over GF(2) with n=544, k=12 and d=256.
This code was found by Heurico 1.16 in 0.5 seconds.