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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+26x^73+71x^74+8x^75+7x^76+10x^77+4x^83+1x^86

The gray image is a code over GF(2) with n=592, k=7 and d=292.
This code was found by Heurico 1.16 in 0.391 seconds.