The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X  1  1 3X+2  1  2  1  1  1  1  1  1  1  1  1 2X X+2 2X+2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2 2X+2  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+1  1  2 X+3  1 2X+3  1 X+2 3X 2X 2X+2  X 3X+1  3 3X+3  1  1  1  1  1  0 X+2  2  X 2X 3X+2 2X+2  X 2X X+2 2X+2 3X 2X X+2 2X+2  X X+1 3X+1 2X+3  3 3X+1  3 3X+3  1  0  2  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X  0 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X  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+14x^72+288x^73+94x^74+224x^75+144x^76+224x^77+32x^79+1x^80+1x^98+1x^114

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 0.266 seconds.