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

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

Homogenous weight enumerator: w(x)=1x^0+66x^72+304x^74+256x^75+360x^76+16x^78+20x^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 0.516 seconds.