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

generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+170x^77+82x^78+330x^79+210x^80+466x^81+485x^82+726x^83+470x^84+428x^85+233x^86+218x^87+20x^88+138x^89+23x^90+68x^91+2x^92+14x^93+9x^94+2x^99+1x^144

The gray image is a code over GF(2) with n=664, k=12 and d=308.
This code was found by Heurico 1.16 in 4.44 seconds.