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

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+29x^78+70x^79+6x^80+4x^81+10x^82+2x^83+1x^84+4x^87+1x^98

The gray image is a code over GF(2) with n=632, k=7 and d=312.
This code was found by Heurico 1.16 in 0.5 seconds.