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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+148x^67+75x^68+92x^69+32x^70+140x^71+15x^72+4x^73+1x^76+4x^84

The gray image is a code over GF(2) with n=552, k=9 and d=268.
This code was found by Heurico 1.16 in 0.313 seconds.