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

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

Homogenous weight enumerator: w(x)=1x^0+72x^73+11x^74+16x^75+12x^76+4x^78+3x^80+8x^81+1x^90

The gray image is a code over GF(2) with n=296, k=7 and d=146.
This code was found by Heurico 1.16 in 0.741 seconds.