The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+122x^77+355x^78+474x^79+437x^80+474x^81+493x^82+440x^83+431x^84+370x^85+283x^86+124x^87+41x^88+42x^89+2x^90+1x^92+2x^102+2x^103+1x^112+1x^122

The gray image is a code over GF(2) with n=656, k=12 and d=308.
This code was found by Heurico 1.16 in 0.703 seconds.