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

generates a code of length 74 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+15x^72+222x^74+15x^76+2x^90+1x^116

The gray image is a code over GF(2) with n=592, k=8 and d=288.
This code was found by Heurico 1.16 in 0.235 seconds.