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

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

Homogenous weight enumerator: w(x)=1x^0+3x^74+22x^75+3x^76+1x^78+2x^79

The gray image is a code over GF(2) with n=292, k=5 and d=148.
This code was found by Heurico 1.16 in 0.176 seconds.