The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+104x^78+264x^79+277x^80+240x^81+381x^82+192x^83+187x^84+240x^85+118x^86+24x^87+12x^88+3x^90+1x^92+2x^98+2x^116

The gray image is a code over GF(2) with n=656, k=11 and d=312.
This code was found by Heurico 1.16 in 0.641 seconds.