The generator matrix

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

generates a code of length 69 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+69x^56+152x^57+254x^58+352x^59+464x^60+592x^61+592x^62+722x^63+783x^64+842x^65+921x^66+942x^67+1002x^68+962x^69+1066x^70+988x^71+927x^72+884x^73+720x^74+708x^75+604x^76+524x^77+444x^78+338x^79+235x^80+138x^81+97x^82+46x^83+10x^84+2x^85+2x^86+1x^128

The gray image is a code over GF(2) with n=138, k=14 and d=56.
This code was found by Heurico 1.16 in 77.2 seconds.