The generator matrix

 1  0  0  1  1  1 2X+2 2X  0  2  1  1  1  1  X  1  1 3X+2 3X  1  1  1  X X+2  1  1 3X  1  1  1  2 2X+2  1  1 3X+2  1  1  1  1  0 2X+2 3X  1  1  1  1 X+2  0 2X  1 3X+2  1  0  1  2 3X  1  1 2X+2  1  X  1  1  1  1  1  1  1  1  1  0  1  2 2X+2  1  1 3X  0  1  1  1  1  1
 0  1  0  0  3 2X+3  1 X+2  1  1 2X+2  2 2X+1 2X+1 3X+2  X X+1  1  1 3X+1 X+2 3X+3  0  1 X+2 3X+1  1 X+2  3 2X  1 3X  X 2X+1  1 X+3  0 2X+2 X+3  X  1  1 3X+1 3X+1 2X 3X+2 2X+2 2X  1 2X+1 3X 3X  1 2X+3  1  2  2  3  1 2X+2  1 3X+2 3X  3 3X 2X 2X+2 2X+3  0  3  2 2X  1 2X X+3 3X  1  1 X+3 3X+2 X+1 3X+1  0
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1 3X  1 2X+3 X+2  1 X+1 3X+3 3X  1 2X 2X  X  1  0 3X  3 X+1  1 2X+1  X  X  1 3X  2 3X+3 X+1  0 3X+1  X  1 2X+2 3X+3 2X+3 2X 2X 3X+3  1  1 3X  1  1 2X+2 2X+3 3X 2X  1 X+3 X+2 X+3 3X X+2 3X+2 X+2 X+3 2X+3  3 2X+3  3 X+2 X+3  1 2X+3 3X+3  1  2  0 3X  1  3 X+1 2X+2 X+2 2X
 0  0  0  2  2  0  2 2X+2  2 2X  2  0  0  2 2X+2 2X+2 2X+2  0  0  0 2X  2 2X 2X+2 2X+2  2  2  2 2X 2X 2X+2  0 2X  2 2X+2 2X 2X+2  0  0 2X 2X+2 2X 2X 2X+2  2  0  0  2  0 2X+2  0  2 2X+2 2X 2X 2X+2 2X+2 2X+2 2X 2X+2  2 2X  0 2X 2X 2X+2  2  2 2X  0 2X 2X 2X+2  2  2  2  0  2  0  0  0 2X+2 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+182x^77+819x^78+1146x^79+1816x^80+1664x^81+2042x^82+1850x^83+2003x^84+1406x^85+1317x^86+680x^87+655x^88+318x^89+206x^90+136x^91+77x^92+24x^93+11x^94+10x^95+8x^96+6x^97+4x^98+2x^99+1x^102

The gray image is a code over GF(2) with n=664, k=14 and d=308.
This code was found by Heurico 1.16 in 4.34 seconds.