The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^29+107x^30+234x^31+287x^32+310x^33+441x^34+532x^35+508x^36+552x^37+648x^38+758x^39+736x^40+614x^41+599x^42+586x^43+428x^44+242x^45+227x^46+168x^47+80x^48+44x^49+23x^50+26x^51+8x^52+6x^53+2x^54+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 1.10 in 1.81 seconds.