The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+456x^79+336x^80+752x^81+348x^82+692x^83+289x^84+432x^85+224x^86+352x^87+75x^88+72x^89+4x^90+28x^91+1x^92+8x^93+8x^95+16x^97+2x^116

The gray image is a code over GF(2) with n=664, k=12 and d=316.
This code was found by Heurico 1.16 in 16.6 seconds.