The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+34x^27+154x^28+270x^29+485x^30+652x^31+889x^32+1190x^33+1541x^34+1824x^35+2241x^36+2704x^37+2791x^38+2944x^39+2856x^40+2716x^41+2444x^42+1998x^43+1622x^44+1222x^45+793x^46+544x^47+376x^48+206x^49+123x^50+64x^51+47x^52+12x^53+11x^54+4x^55+6x^56+4x^58

The gray image is a code over GF(2) with n=78, k=15 and d=27.
This code was found by Heurico 1.16 in 79.9 seconds.