The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+175x^78+314x^79+435x^80+478x^81+515x^82+404x^83+462x^84+386x^85+402x^86+302x^87+163x^88+30x^89+8x^90+4x^91+8x^92+2x^93+1x^96+2x^104+2x^106+1x^114+1x^118

The gray image is a code over GF(2) with n=664, k=12 and d=312.
This code was found by Heurico 1.16 in 0.734 seconds.