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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+7x^72+48x^73+7x^74+1x^82

The gray image is a code over GF(2) with n=288, k=6 and d=144.
This code was found by Heurico 1.16 in 0.168 seconds.