The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  1  1  1  2  1  0  2  1  2  2  0  1  2  1  1  2  2  0  1  1  1  0  2
 0  1  0  0  0  0  0  0  0  0  0  2  3  1  1  3  2  1  2  1  1  1  3  2  1  0  1  1  1  1  2  1  1  0
 0  0  1  0  0  0  1  1  1  2  2  0  2  2  0  3  1  3  2  1  1  0  0  1  3  1  2  0  2  0  3  3  1  1
 0  0  0  1  0  1  1  0  3  2  0  3  3  2  3  2  3  0  2  0  3  2  2  3  2  2  1  2  2  1  1  3  1  0
 0  0  0  0  1  1  2  3  1  1  1  2  3  2  1  0  2  0  2  1  3  3  1  0  0  2  2  0  1  3  1  1  2  1
 0  0  0  0  0  2  0  2  2  2  0  2  0  0  0  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  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+64x^27+113x^28+132x^29+164x^30+170x^31+181x^32+150x^33+151x^34+154x^35+160x^36+174x^37+121x^38+110x^39+84x^40+50x^41+41x^42+14x^43+3x^44+6x^45+3x^46+2x^48

The gray image is a code over GF(2) with n=68, k=11 and d=27.
This code was found by Heurico 1.16 in 0.226 seconds.