The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^73+6x^74+4x^75+7x^76+6x^77+1x^78+1x^82

The gray image is a code over GF(2) with n=292, k=6 and d=146.
This code was found by Heurico 1.16 in 0.266 seconds.