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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+320x^73+129x^74+476x^75+337x^76+544x^77+619x^78+568x^79+318x^80+328x^81+111x^82+172x^83+14x^84+112x^85+5x^86+32x^87+1x^88+8x^89+1x^132

The gray image is a code over GF(2) with n=624, k=12 and d=292.
This code was found by Heurico 1.16 in 146 seconds.