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 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2  0 X^2 X^2 X^2+2  2 X^2+2  0 X^2  0  0  2 X^2+2 X^2+2  2 X^2 X^2+2  2  2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2  2 X^2+2  2 X^2  2 X^2+2  2 X^2  2  2 X^2+2 X^2  0  2 X^2 X^2+2  2 X^2+2  2 X^2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2 X^2+2  2  2 X^2 X^2  2  0 X^2 X^2 X^2 X^2+2  2 X^2 X^2+2  2  2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2+2  2  0 X^2+2  0 X^2 X^2+2  0  2 X^2 X^2  0  0 X^2+2 X^2  0  0 X^2 X^2  0  2 X^2+2  0  2
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  2  0  2  0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  2  0  0  0  2  2  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  0  0  2  0  2  0  2  2  0  2  0  2  0  0  2  0  2  2  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  0  0  0  0  2  0  2  0

generates a code of length 75 over Z4[X]/(X^3+2,2X) 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.