The generator matrix

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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+144x^77+126x^78+480x^79+126x^80+144x^81+1x^94+1x^96+1x^126

The gray image is a code over GF(2) with n=632, k=10 and d=308.
This code was found by Heurico 1.16 in 0.907 seconds.