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

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

Homogenous weight enumerator: w(x)=1x^0+228x^72+128x^73+320x^74+128x^75+208x^76+10x^80+1x^128

The gray image is a code over GF(2) with n=592, k=10 and d=288.
This code was found by Heurico 1.16 in 0.266 seconds.