The generator matrix

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

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+128x^77+421x^78+260x^79+672x^80+304x^81+586x^82+412x^83+591x^84+172x^85+344x^86+82x^87+63x^88+36x^89+1x^90+12x^91+1x^92+2x^94+2x^95+4x^98+1x^114+1x^118

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 0.859 seconds.