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

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+182x^74+128x^75+412x^76+128x^77+164x^78+2x^80+6x^82+1x^144

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 0.625 seconds.