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

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

Homogenous weight enumerator: w(x)=1x^0+89x^72+64x^73+216x^74+64x^75+56x^76+16x^78+2x^80+2x^84+2x^96

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 0.407 seconds.