The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+142x^77+763x^78+866x^79+1307x^80+994x^81+1076x^82+740x^83+632x^84+458x^85+460x^86+266x^87+197x^88+102x^89+138x^90+16x^91+30x^92+1x^94+1x^96+2x^98

The gray image is a code over GF(2) with n=656, k=13 and d=308.
This code was found by Heurico 1.16 in 1.22 seconds.