The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+58x^56+92x^57+185x^58+268x^59+360x^60+364x^61+390x^62+372x^63+393x^64+454x^65+426x^66+476x^67+477x^68+526x^69+479x^70+466x^71+411x^72+418x^73+354x^74+358x^75+271x^76+154x^77+163x^78+98x^79+69x^80+36x^81+38x^82+10x^83+8x^84+4x^85+12x^86+1x^98

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 10.4 seconds.