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  2  2  2  1  1  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  2  0  2  2  2  0  2  2  2  2  2  0  2  0  2  2  2  2  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  0  0  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  2  0  2  2  0  0  0  2  2  0  0  0  0  0  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  0  2  2  0  2  2  2  0  2  2  2  2  0  2  0  2  2  2  0  2  2  2  0  0  0  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  0  2  2  0  0  0  0  0  0  0  0  2  2  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  2  2  0  2  2  2  0  0  0  2  2  2  0  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  0  0

generates a code of length 72 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+36x^68+32x^70+117x^72+32x^74+36x^76+1x^80+1x^136

The gray image is a code over GF(2) with n=144, k=8 and d=68.
This code was found by Heurico 1.16 in 0.135 seconds.