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  1  1  X  1  1  X  1  1  X  1  1  X  X  1  X  1  X  X  2  1  X  X  1  2  X  X  X  2  1  X 2X  2  0  X  2  2  X  2 2X  0 2X  X  1  2  2 2X  2  1
 0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X  0  0  0

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+1x^74+24x^75+1x^76+4x^77+1x^78

The gray image is a code over GF(2) with n=584, k=5 and d=296.
This code was found by Heurico 1.16 in 0.219 seconds.