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

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

Homogenous weight enumerator: w(x)=1x^0+3x^74+54x^75+3x^76+1x^78+2x^79

The gray image is a code over GF(2) with n=592, k=6 and d=296.
This code was found by Heurico 1.16 in 0.25 seconds.