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  0  1  1  1  1  1  1  1  1  2  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  X  0 X^2  X  X  0 X^2+2
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0  0  X  X  0  0  X  X  2 X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  2  2  2 X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  2  2 X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X+2 X+2  2  2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  2  2 X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  X X^2+X  X  X  X X^2+X+2  X  X
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2 X^2+X+2  2 X+2 X^2+2  2 X^2+X+2 X+2 X^2+2 X+2 X^2 X^2+X  2  X X^2+2  X X^2+X+2  0  0 X^2+X  X X^2  X  2 X^2+X+2 X+2 X^2+2 X^2+2 X+2 X^2+X+2  2 X^2  X X^2+X  0  0 X^2+X  X X^2+2  X X^2 X^2+2 X+2 X^2  X X+2 X^2  0 X^2+X X^2+X+2  2  2 X^2+X+2 X^2+X  0  X  0  0 X^2+2 X^2+X+2 X^2  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+228x^72+128x^73+320x^74+128x^75+208x^76+10x^80+1x^128

The gray image is a code over GF(2) with n=592, k=10 and d=288.
This code was found by Heurico 1.16 in 0.265 seconds.