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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+3x^76+22x^77+3x^78+2x^81+1x^82

The gray image is a code over GF(2) with n=300, k=5 and d=152.
This code was found by Heurico 1.16 in 0.196 seconds.