The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+197x^26+475x^28+874x^30+1092x^32+1472x^34+1338x^36+1309x^38+788x^40+457x^42+139x^44+40x^46+5x^48+2x^50+1x^54+2x^56

The gray image is a code over GF(2) with n=70, k=13 and d=26.
This code was found by Heurico 1.16 in 5.49 seconds.