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

generates a code of length 77 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+5x^76+104x^77+6x^78+2x^79+4x^81+2x^83+2x^84+1x^86+1x^98

The gray image is a code over GF(2) with n=616, k=7 and d=304.
This code was found by Heurico 1.16 in 0.281 seconds.