The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^26+32x^27+225x^28+252x^29+448x^30+540x^31+907x^32+1108x^33+1385x^34+1976x^35+2260x^36+2740x^37+2914x^38+3128x^39+2858x^40+2696x^41+2351x^42+1936x^43+1494x^44+1188x^45+876x^46+524x^47+388x^48+196x^49+167x^50+56x^51+52x^52+12x^53+18x^54+6x^56+1x^58+1x^60

The gray image is a code over GF(2) with n=78, k=15 and d=26.
This code was found by Heurico 1.16 in 57.2 seconds.