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  0  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  1  1  0
 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  1  2  0

generates a code of length 36 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+6x^34+18x^35+15x^36+12x^37+6x^38+2x^39+1x^42+3x^46

The gray image is a code over GF(2) with n=72, k=6 and d=34.
This code was found by Heurico 1.16 in 0.00462 seconds.