The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+44x^29+115x^30+184x^31+298x^32+336x^33+403x^34+476x^35+570x^36+600x^37+677x^38+720x^39+641x^40+736x^41+603x^42+504x^43+428x^44+284x^45+213x^46+152x^47+97x^48+48x^49+33x^50+12x^51+10x^52+3x^54+3x^56+1x^58

The gray image is a code over GF(2) with n=78, k=13 and d=29.
This code was found by Heurico 1.16 in 41.4 seconds.