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

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

Homogenous weight enumerator: w(x)=1x^0+30x^70+161x^72+128x^73+161x^74+28x^76+1x^82+2x^108

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.