The generator matrix

 1  0  0  1  1  1  2  1  1  1 X^2+X X^2+X X^2+X+2  1  1 X^2+2  X X+2  1  1  1  1  1  1 X^2 X^2 X^2  1 X^2+X  X  1  1  0  X  1  0 X^2+X+2  1  1  0  1 X^2+X+2  1  1  1  1  1  1  1  1  1 X^2+2  1  1 X+2  X  1 X^2+X X+2  2  X  1  1  0  1  X  1  1  1  1  1
 0  1  0 X^2 X^2+3 X^2+1  1 X^2+2  2 X+1  1  0  1 X+3 X+2  1  1  X  3 X^2+X+2  3 X+1 X+3 X+2  1  1  0 X^2+3  1 X^2 X^2+X+2 X^2+1  X  1  0 X^2+X  1  3  2  1 X^2+X+3  1  3 X+1 X^2+2 X^2+X+1  2  1 X^2+X X+2 X+3  1 X^2+1  3 X^2+X+2  1 X^2+X X^2  1  1 X+2 X^2+3 X+2  X X^2+X+3  1  1 X^2+3 X^2+X+1 X^2+1  0
 0  0  1 X^2+X+1 X^2+X+3 X^2+2 X+1 X+2 X^2+3  2 X+1  1 X^2  1 X+2 X^2+1 X+2  1  3 X+3 X^2+X X^2+X+2 X^2+X+3  2  X X+1  1 X^2+1 X^2+1  1  1 X^2+X+2  1 X^2+X+3  0  1 X^2+X+2 X^2+2 X+2 X^2+3 X^2+X+3 X^2  2  1 X^2+1 X+2 X^2+X+3 X^2+X+1 X^2+2 X^2+X+2  2 X^2+2 X^2+3 X+1  1  1  3  1  0 X+2  1 X+3 X^2+X+3  1 X^2+3 X^2  X  0 X^2+3  3  0
 0  0  0  2  2  2  0  2  0  0  2  2  2  0  0  0  2  2  0  2  2  0  2  2  0  2  2  2  0  0  0  0  2  0  2  0  0  2  0  2  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  2  2  0  2  0  0  0  0  0  2  0  2  2  0  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+124x^66+762x^67+716x^68+1412x^69+818x^70+1406x^71+499x^72+906x^73+375x^74+504x^75+233x^76+274x^77+89x^78+44x^79+21x^80+1x^82+4x^83+1x^84+1x^86+1x^88

The gray image is a code over GF(2) with n=568, k=13 and d=264.
This code was found by Heurico 1.16 in 0.828 seconds.