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

generates a code of length 79 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+30x^78+448x^79+30x^80+1x^94+1x^96+1x^126

The gray image is a code over GF(2) with n=632, k=9 and d=312.
This code was found by Heurico 1.16 in 0.828 seconds.