The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  1  2  1  1  1  2  2  1  1  1  2  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  2  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  2  2  2  0  0  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  0  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  0  2  0  0  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  0  2  0  2
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  2  2  2  0  2  2  0  0  2  2  2  2  2  2  2  0  2  2
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  0  2  2  2  0  2  0  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  0  0  0  0  0  2  0  2  0  0  2  0

generates a code of length 35 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+131x^22+256x^24+320x^26+552x^28+1172x^30+2333x^32+3424x^34+3320x^36+2322x^38+1156x^40+576x^42+408x^44+212x^46+90x^48+32x^50+24x^52+3x^54+4x^56

The gray image is a code over GF(2) with n=70, k=14 and d=20.
This code was found by Heurico 1.16 in 14.4 seconds.