The generator matrix

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

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+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.