The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+302x^74+1556x^75+3462x^76+6604x^77+9744x^78+15636x^79+20304x^80+26944x^81+29406x^82+33144x^83+30440x^84+28080x^85+20166x^86+15752x^87+9528x^88+5564x^89+2886x^90+1540x^91+536x^92+284x^93+130x^94+52x^95+39x^96+12x^97+18x^98+6x^100+4x^102+4x^104

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 807 seconds.