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

generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+336x^72+48x^73+610x^74+184x^75+865x^76+304x^77+732x^78+192x^79+375x^80+32x^81+222x^82+8x^83+138x^84+32x^86+12x^88+4x^90+1x^124

The gray image is a code over GF(2) with n=616, k=12 and d=288.
This code was found by Heurico 1.16 in 1.38 seconds.