The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+83x^76+186x^77+302x^78+354x^79+485x^80+546x^81+459x^82+498x^83+326x^84+258x^85+246x^86+126x^87+82x^88+46x^89+31x^90+30x^91+23x^92+4x^93+9x^94+1x^126

The gray image is a code over GF(2) with n=656, k=12 and d=304.
This code was found by Heurico 1.16 in 0.937 seconds.