The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+301x^74+1594x^75+3542x^76+5632x^77+8055x^78+10608x^79+12714x^80+15136x^81+15791x^82+15376x^83+13258x^84+11036x^85+7766x^86+4940x^87+2709x^88+1346x^89+720x^90+278x^91+120x^92+80x^93+37x^94+20x^95+6x^96+2x^97+2x^98+2x^100

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 188 seconds.