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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+337x^64+24x^65+508x^66+328x^67+623x^68+600x^69+600x^70+280x^71+382x^72+48x^73+244x^74+96x^76+24x^78+1x^116

The gray image is a code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 17 seconds.