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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+38x^76+112x^77+217x^78+300x^79+226x^80+88x^81+20x^82+12x^83+6x^84+3x^86+1x^152

The gray image is a code over GF(2) with n=632, k=10 and d=304.
This code was found by Heurico 1.16 in 0.703 seconds.