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  1  1  1  1  2  1  1  1  1  0  X  X  0  X  X
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2 X^2+X  0 X+2 X^2+2 X+2  2 X^2 X^2+X+2 X+2  0 X^2+X X^2+2 X^2+X  0 X^2+2 X+2 X^2+X+2  0 X+2 X^2+2 X^2+X+2  2  X X^2 X^2+X  0  0  X X^2+2 X^2+2 X^2+X+2  X  2 X^2 X^2+X X^2+X X^2  2 X+2 X+2  0  2  0  2 X^2+X X^2+X+2 X^2+X X^2+X+2 X^2+2 X^2+2 X^2 X^2  2 X+2 X+2  X  X  X X^2+X X+2  X  0  0
 0  0  2  0  0  0  2  0  2  0  2  2  2  0  2  2  0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  0  0  2  2  0  0  2  0  2  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  0  0  0  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  0  2  0  0  0  2  2  0
 0  0  0  0  2  0  2  2  2  0  0  2  2  2  0  2  2  2  0  2  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  2  0  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  0  2  0  0  2  2  0  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+44x^66+318x^68+256x^69+328x^70+256x^71+510x^72+108x^74+194x^76+32x^78+1x^128

The gray image is a code over GF(2) with n=568, k=11 and d=264.
This code was found by Heurico 1.16 in 0.422 seconds.