The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+38x^25+117x^26+264x^27+466x^28+648x^29+937x^30+1390x^31+1887x^32+2430x^33+3201x^34+3852x^35+4401x^36+4956x^37+5234x^38+5578x^39+5377x^40+4936x^41+4590x^42+3996x^43+3276x^44+2412x^45+1901x^46+1326x^47+854x^48+626x^49+361x^50+224x^51+113x^52+80x^53+40x^54+10x^55+9x^56+2x^57+3x^58

The gray image is a code over GF(2) with n=78, k=16 and d=25.
This code was found by Heurico 1.10 in 94.7 seconds.