The generator matrix

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

generates a code of length 65 over Z4 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+66x^55+150x^56+168x^57+168x^58+220x^59+232x^60+210x^61+251x^62+238x^63+296x^64+258x^65+251x^66+252x^67+196x^68+246x^69+185x^70+176x^71+111x^72+102x^73+91x^74+62x^75+56x^76+32x^77+44x^78+8x^79+13x^80+8x^81+2x^82+2x^83+1x^88

The gray image is a code over GF(2) with n=130, k=12 and d=55.
This code was found by Heurico 1.16 in 2.26 seconds.