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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  X  X  1
 0  2  0 2X+2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X+2  2  0 2X+2 2X+2  2 2X 2X+2 2X+2  0  2  0  0 2X 2X 2X+2  2 2X  0  2  2 2X+2 2X  2  0  2 2X+2  0  0 2X 2X  0 2X 2X+2  2  0  0  2  2 2X  0  0
 0  0  2 2X+2  0  2 2X+2  0 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X  0  2 2X+2  0  0  2 2X+2  0 2X+2 2X+2  0  2 2X  2  0 2X+2 2X+2  2 2X+2 2X  0 2X 2X  0  0  2  2 2X+2 2X+2 2X 2X  2  2  2 2X+2  0  0 2X 2X  0  0 2X+2 2X+2  0  0  2 2X+2 2X 2X+2  2  0
 0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0  0  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+21x^72+48x^73+9x^74+352x^75+10x^76+46x^77+22x^78+1x^82+2x^109

The gray image is a code over GF(2) with n=600, k=9 and d=288.
This code was found by Heurico 1.16 in 0.422 seconds.