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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+23x^70+24x^71+139x^72+148x^73+132x^74+14x^75+20x^76+4x^77+5x^78+2x^107

The gray image is a code over GF(2) with n=584, k=9 and d=280.
This code was found by Heurico 1.16 in 0.375 seconds.