The generator matrix

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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+51x^72+170x^73+112x^74+128x^75+10x^76+10x^77+14x^78+8x^79+2x^80+2x^81+2x^85+2x^86

The gray image is a code over GF(2) with n=592, k=9 and d=288.
This code was found by Heurico 1.16 in 0.25 seconds.