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  X  1  1  1  1  1  X  1  1  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0 2X+2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  0 2X+2 2X+2  2 2X  2  0 2X+2  0  0 2X  2  2 2X 2X+2  2 2X 2X 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X 2X  2 2X 2X+2 2X  2 2X 2X+2 2X 2X  2 2X+2  0 2X 2X+2  2 2X  2 2X 2X+2
 0  0  2 2X+2  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0 2X 2X+2  2 2X 2X 2X+2  2 2X  2 2X 2X 2X+2 2X+2 2X  0 2X+2 2X+2 2X+2  2 2X 2X+2  2 2X 2X 2X+2 2X 2X+2  2 2X 2X 2X+2  2 2X  0  2  2 2X  0  2  0 2X+2  2  0 2X 2X+2 2X+2  0  0  2 2X+2  0  0 2X+2 2X+2  0 2X  2  0 2X
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0  0 2X  0  0  0  0  0  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0  0  0 2X  0  0  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0  0  0  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+72x^72+120x^74+640x^75+124x^76+56x^78+10x^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 123 seconds.