The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+29x^28+38x^29+46x^30+48x^31+36x^32+46x^33+48x^34+48x^35+32x^36+34x^37+24x^38+32x^39+24x^40+10x^41+8x^42+3x^44+2x^46+3x^48

The gray image is a code over GF(2) with n=68, k=9 and d=28.
This code was found by Heurico 1.16 in 0.0234 seconds.