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

generates a code of length 77 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+64x^75+91x^76+256x^77+64x^79+31x^80+2x^84+1x^92+2x^100

The gray image is a code over GF(2) with n=616, k=9 and d=300.
This code was found by Heurico 1.16 in 0.984 seconds.