The generator matrix

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

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+50x^78+326x^79+335x^80+334x^81+224x^82+180x^83+189x^84+244x^85+60x^86+46x^87+26x^88+18x^89+1x^90+4x^93+8x^96+1x^106+1x^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 0.422 seconds.