The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^73+18x^74+6x^75+1x^76+1x^78+2x^79+2x^80+1x^82

The gray image is a code over GF(2) with n=584, k=6 and d=292.
This code was found by Heurico 1.16 in 0.265 seconds.