The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  2  1  1  0  1  1  0  1  1  2  1  1  2  1  1  0  1  1  0  1  1  1  1  2  2  2  2  0  0  1  1  1  1  0  2  1  1  1  1  2  2  0  0  2  2  2  0  0  2  2  0  1  1  0  1  1  2  2
 0  1  1  0  3  1  2  3  1  2  1  1  0  3  1  0  3  1  2  1  1  2  1  1  0  3  1  0  3  1  2  2  1  1  1  1  0  2  2  0  0  2  3  1  1  1  0  2  3  1  0  2  2  1  1  0  2  2  0  0  2  2  0  3  1  2  1  1  0
 0  0  2  2  0  2  2  2  2  0  0  0  0  0  2  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  2  2  2  2  0  0  0  0  0  2  0  0  2  2

generates a code of length 69 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+15x^70+15x^72+1x^78

The gray image is a code over GF(2) with n=138, k=5 and d=70.
This code was found by Heurico 1.16 in 0.0702 seconds.