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

generates a code of length 75 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+44x^72+32x^73+272x^74+320x^75+284x^76+32x^77+32x^78+6x^80+1x^144

The gray image is a code over GF(2) with n=600, k=10 and d=288.
This code was found by Heurico 1.16 in 0.438 seconds.