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

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+68x^65+132x^66+120x^67+862x^68+60x^69+540x^70+12x^71+24x^72+64x^73+104x^74+60x^75+1x^136

The gray image is a code over GF(2) with n=552, k=11 and d=260.
This code was found by Heurico 1.16 in 0.516 seconds.