The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  2  1  1 X^2+X+2  1  1 X^2  1  1  X  X  X  0  X  X  0  2 X^2+2  2  1  1  1  1  1  X  1  X  1  1  1  1 X^2+X  1  1  0 X^2+2 X+2
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X  3  1 X^2+2 X^2+X+3  1 X+2 X^2+1  1  2 X+3  1 X^2+X+2 X^2+3  1 X^2 X^2+X+1  1  X  1  1  0 X^2+X  X X^2+2 X+2  1  X  1  1  0 X^2+3 X+3 X^2+X+2 X+2 X^2+2 X^2+X+3 X^2+X X+3 X^2+X+3 X^2+3  2  1 X^2+X+1 X+1  X  1  1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  0  2  2  0  2  0  0  2  0  0  2  2  2  0  0  2  0  2  0  0  2  0
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  2  2  0  0  0  2  2  2
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  0  2  0  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  2

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+562x^72+594x^74+389x^76+328x^78+147x^80+22x^82+2x^84+1x^88+1x^92+1x^120

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 59.1 seconds.