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

generates a code of length 69 over Z4[X]/(X^3+2,2X) 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 0.531 seconds.