The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+88x^27+132x^28+192x^29+280x^30+248x^31+279x^32+324x^33+345x^34+340x^35+324x^36+324x^37+319x^38+276x^39+220x^40+172x^41+103x^42+68x^43+35x^44+12x^45+9x^46+4x^47+1x^60

The gray image is a code over GF(2) with n=70, k=12 and d=27.
This code was found by Heurico 1.16 in 1.28 seconds.