The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+256x^78+240x^79+500x^80+320x^81+535x^82+416x^83+533x^84+320x^85+470x^86+240x^87+241x^88+17x^90+1x^92+1x^94+1x^96+1x^102+2x^108+1x^112

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 0.781 seconds.