The generator matrix

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

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+480x^77+224x^78+326x^79+109x^80+312x^81+136x^82+332x^83+25x^84+76x^85+14x^86+6x^87+4x^89+1x^100+1x^102+1x^110

The gray image is a code over GF(2) with n=640, k=11 and d=308.
This code was found by Heurico 1.16 in 36.3 seconds.