The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+87x^28+98x^29+319x^30+360x^31+525x^32+618x^33+722x^34+964x^35+1059x^36+1296x^37+1362x^38+1432x^39+1356x^40+1416x^41+1109x^42+1020x^43+801x^44+566x^45+495x^46+300x^47+246x^48+94x^49+72x^50+16x^51+21x^52+8x^53+16x^54+4x^55+1x^58

The gray image is a code over GF(2) with n=78, k=14 and d=28.
This code was found by Heurico 1.16 in 31.9 seconds.