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

generates a code of length 76 over Z4[X]/(X^3+2,2X) 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 0.61 seconds.