The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+286x^66+1370x^67+2772x^68+4230x^69+5434x^70+7214x^71+7640x^72+8016x^73+8047x^74+7030x^75+5182x^76+3902x^77+2129x^78+1170x^79+655x^80+308x^81+83x^82+32x^83+22x^84+8x^85+5x^86

The gray image is a code over GF(2) with n=584, k=16 and d=264.
This code was found by Heurico 1.16 in 42.8 seconds.