The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+416x^75+1679x^76+3312x^77+5695x^78+7928x^79+10743x^80+12850x^81+15346x^82+15608x^83+15374x^84+13044x^85+10675x^86+7748x^87+5071x^88+2860x^89+1497x^90+592x^91+348x^92+116x^93+98x^94+28x^95+29x^96+10x^97+1x^98+3x^100

The gray image is a code over GF(2) with n=664, k=17 and d=300.
This code was found by Heurico 1.16 in 183 seconds.