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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+18x^68+16x^69+24x^70+48x^71+298x^72+48x^73+24x^74+16x^75+18x^76+1x^144

The gray image is a code over GF(2) with n=288, k=9 and d=136.
This code was found by Heurico 1.16 in 0.191 seconds.