The generator matrix

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

generates a code of length 65 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+26x^53+115x^54+184x^55+236x^56+334x^57+348x^58+380x^59+371x^60+438x^61+484x^62+468x^63+475x^64+492x^65+556x^66+440x^67+453x^68+450x^69+423x^70+400x^71+280x^72+226x^73+197x^74+140x^75+94x^76+78x^77+50x^78+36x^79+8x^80+4x^81+2x^82+1x^84+1x^90+1x^92

The gray image is a code over GF(2) with n=130, k=13 and d=53.
This code was found by Heurico 1.10 in 3.65 seconds.