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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+17x^74+72x^75+88x^76+40x^77+12x^78+12x^79+5x^80+3x^82+4x^83+2x^84

The gray image is a code over GF(2) with n=608, k=8 and d=296.
This code was found by Heurico 1.16 in 0.422 seconds.