The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^26+42x^27+96x^28+112x^29+152x^30+168x^31+152x^32+192x^33+154x^34+188x^35+154x^36+176x^37+122x^38+104x^39+93x^40+32x^41+34x^42+10x^43+14x^44+6x^46+1x^48+1x^56

The gray image is a code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.16 in 0.233 seconds.