The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+13x^38+32x^39+14x^40+2x^46+1x^48+1x^54

The gray image is a code over GF(2) with n=78, k=6 and d=38.
This code was found by Heurico 1.16 in 0.00917 seconds.