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

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+80x^73+141x^74+8x^75+10x^76+4x^77+2x^78+5x^80+4x^89+1x^90

The gray image is a code over GF(2) with n=592, k=8 and d=292.
This code was found by Heurico 1.16 in 9.33 seconds.