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

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+154x^79+116x^80+210x^81+272x^82+588x^83+291x^84+180x^85+48x^86+114x^87+39x^88+26x^89+8x^91+1x^156

The gray image is a code over GF(2) with n=664, k=11 and d=316.
This code was found by Heurico 1.16 in 0.703 seconds.