The generator matrix

 1  0  1  1  1 X^2+X+2  1  X  1  2  1  1 X^2  1  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1 X+2  1  0  1  1  1  1  1  2 X^2+X+2  1  1  1  1  1  2  X X^2  1  1 X^2+X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1 X^2  1  1  X
 0  1 X+1 X^2+X X^2+3  1 X^2+2  1 X^2+X+1  1 X+2  1  1  2 X+1 X^2+X+2  1 X^2+X+3 X^2  1  X  1 X+1 X^2+X+3 X^2+1  3  0  1 X^2+1  1 X^2+X+2 X+3 X^2 X^2+3 X^2+X  1  1  3 X^2+2 X+2 X^2+X X+3  1  1  1  2  1  1  0  X X^2 X+2  2 X^2 X^2+2 X+2  X X^2 X^2 X+2 X^2+X+2 X^2+X X^2+X X^2+2 X^2+3 X^2+X X^2  1 X^2  0 X+2
 0  0 X^2  0 X^2+2 X^2  0 X^2 X^2+2 X^2+2  0 X^2 X^2+2 X^2  2 X^2+2  0  2 X^2  0 X^2+2  0  2  2  0  2  0  0  2  0 X^2+2 X^2 X^2 X^2+2  2 X^2 X^2  0  0  2 X^2 X^2  2 X^2 X^2 X^2+2 X^2+2  2 X^2+2 X^2+2  2 X^2 X^2  0  2  0  0  2  0 X^2  2  2 X^2 X^2  2 X^2+2 X^2+2 X^2 X^2 X^2+2  0
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  2  0  2  0  2  0  0  0  2  0  2  0  0  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  2  0  0  2  0  0  0  2  0  0  0
 0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  0  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  0  0  0  0  2  2  0  0  2  2  2

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+121x^66+292x^67+361x^68+560x^69+548x^70+572x^71+418x^72+448x^73+339x^74+236x^75+97x^76+48x^77+8x^78+20x^79+11x^80+6x^82+6x^84+2x^86+2x^100

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 0.578 seconds.