The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+74x^27+111x^28+124x^29+170x^30+148x^31+168x^32+174x^33+164x^34+152x^35+169x^36+166x^37+106x^38+124x^39+79x^40+42x^41+40x^42+14x^43+16x^44+6x^45

The gray image is a code over GF(2) with n=68, k=11 and d=27.
This code was found by Heurico 1.10 in 0.11 seconds.