The generator matrix

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

generates a code of length 65 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+150x^54+512x^56+745x^58+805x^60+942x^62+989x^64+965x^66+929x^68+865x^70+623x^72+346x^74+212x^76+79x^78+22x^80+4x^82+2x^84+1x^96

The gray image is a code over GF(2) with n=130, k=13 and d=54.
This code was found by Heurico 1.16 in 9.75 seconds.