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

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+66x^77+105x^78+86x^79+226x^80+238x^81+623x^82+220x^83+215x^84+104x^85+103x^86+46x^87+5x^88+6x^89+1x^90+2x^93+1x^156

The gray image is a code over GF(2) with n=656, k=11 and d=308.
This code was found by Heurico 1.16 in 1.12 seconds.