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

generates a code of length 72 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+56x^70+112x^71+189x^72+100x^73+24x^74+4x^75+18x^76+2x^77+2x^79+2x^81+2x^83

The gray image is a code over GF(2) with n=576, k=9 and d=280.
This code was found by Heurico 1.16 in 0.218 seconds.