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

generates a code of length 71 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+361x^66+40x^67+433x^68+336x^69+659x^70+544x^71+641x^72+304x^73+391x^74+56x^75+214x^76+85x^78+17x^80+8x^82+5x^84+1x^120

The gray image is a code over GF(2) with n=568, k=12 and d=264.
This code was found by Heurico 1.16 in 0.656 seconds.