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

generates a code of length 78 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+218x^76+128x^77+364x^78+128x^79+146x^80+36x^82+2x^84+1x^144

The gray image is a code over GF(2) with n=624, k=10 and d=304.
This code was found by Heurico 1.16 in 0.329 seconds.