The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+112x^65+602x^66+760x^67+664x^68+512x^69+348x^70+324x^71+272x^72+188x^73+119x^74+68x^75+92x^76+20x^77+10x^78+3x^80+1x^82

The gray image is a code over GF(2) with n=552, k=12 and d=260.
This code was found by Heurico 1.16 in 0.297 seconds.