The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+364x^74+1508x^75+3466x^76+6264x^77+10038x^78+15516x^79+21188x^80+25856x^81+30610x^82+32100x^83+30744x^84+27152x^85+21016x^86+15472x^87+9781x^88+5536x^89+3012x^90+1392x^91+663x^92+232x^93+138x^94+28x^95+34x^96+16x^97+6x^98+11x^100

The gray image is a code over GF(2) with n=664, k=18 and d=296.
This code was found by Heurico 1.16 in 735 seconds.