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

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+232x^74+192x^75+216x^76+192x^77+144x^78+38x^80+8x^82+1x^128

The gray image is a code over GF(2) with n=608, k=10 and d=296.
This code was found by Heurico 1.16 in 8.11 seconds.