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

generates a code of length 77 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+23x^74+74x^76+320x^77+68x^78+20x^80+3x^82+1x^88+2x^110

The gray image is a code over GF(2) with n=616, k=9 and d=296.
This code was found by Heurico 1.16 in 0.453 seconds.