The generator matrix

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

generates a code of length 65 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+37x^56+60x^57+131x^58+152x^59+128x^60+162x^61+125x^62+146x^63+123x^64+106x^65+119x^66+104x^67+118x^68+96x^69+65x^70+66x^71+65x^72+58x^73+54x^74+28x^75+30x^76+26x^77+18x^78+16x^79+10x^80+4x^81

The gray image is a code over GF(2) with n=130, k=11 and d=56.
This code was found by Heurico 1.16 in 0.563 seconds.