The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+400x^74+1686x^75+3450x^76+5190x^77+7923x^78+10590x^79+13491x^80+14842x^81+16152x^82+15158x^83+13922x^84+10398x^85+7430x^86+4732x^87+2870x^88+1564x^89+725x^90+264x^91+152x^92+64x^93+38x^94+18x^95+2x^96+6x^97+3x^98+1x^102

The gray image is a code over GF(2) with n=656, k=17 and d=296.
This code was found by Heurico 1.16 in 217 seconds.