The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+65x^26+172x^27+369x^28+628x^29+888x^30+1328x^31+1704x^32+2400x^33+3061x^34+3638x^35+4550x^36+5128x^37+5751x^38+5948x^39+5689x^40+5260x^41+4589x^42+3916x^43+3133x^44+2432x^45+1710x^46+1196x^47+847x^48+484x^49+291x^50+178x^51+84x^52+52x^53+27x^54+8x^55+7x^56+2x^58

The gray image is a code over GF(2) with n=78, k=16 and d=26.
This code was found by Heurico 1.10 in 99.6 seconds.