The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1  1  2  1  1 X^2+X+2  1  1 X+2  1  1  2 X^2+X  1  1  1  1 X^2  1  1  X  1  1 X^2  1  1  X  1  1  0  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  1  1  2  1 X^2+X  X  1  1 X^2 X+2
 0  1 X+1 X^2+X+2 X^2+1  1  2 X^2+X+1  1 X^2+2 X+1  1  X  3  1 X^2+X X^2+3  1 X+2 X^2+X+3  1  1 X^2+X+2 X+3  2 X^2+3  1 X^2  1  1 X^2 X^2+X+1  1  X  1  1 X+1  0  1 X+2 X^2+1  1 X^2+2  3  1 X^2+X  1 X^2+X+3  0 X^2+X X^2+2 X+2  2  2 X^2+X X+2 X^2+X X^2 X^2+X+2 X^2  X X^2  2  X  0 X^2 X^2+3  1 X+3  1 X^2 X^2+X+3  1  1  1
 0  0 X^2 X^2  2 X^2 X^2+2 X^2+2  2  2  0 X^2+2 X^2+2  0 X^2+2  0 X^2+2  0  2  2 X^2  2 X^2+2 X^2+2 X^2 X^2 X^2 X^2 X^2 X^2 X^2+2 X^2 X^2+2 X^2 X^2+2 X^2+2  2  2  2  0  0  0  0  2  0  2  2  0 X^2+2 X^2+2 X^2 X^2+2 X^2  2 X^2 X^2  0  0  2 X^2+2  2  0  2  0  2  0  2  0 X^2+2 X^2+2  2 X^2+2  2  0 X^2+2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  0  2  0  2  0  2  2  2  0  0  2  0  2  0  2  2  2  0  0  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  2  0  2  2  2  2  2  0  0  2  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+568x^72+464x^74+592x^76+272x^78+147x^80+2x^96+2x^104

The gray image is a code over GF(2) with n=600, k=11 and d=288.
This code was found by Heurico 1.16 in 112 seconds.