The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+142x^26+357x^28+542x^30+666x^32+676x^34+719x^36+526x^38+293x^40+122x^42+44x^44+8x^46

The gray image is a code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.10 in 0.344 seconds.