The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+90x^27+134x^28+188x^29+255x^30+276x^31+303x^32+286x^33+363x^34+336x^35+325x^36+310x^37+293x^38+332x^39+219x^40+154x^41+105x^42+54x^43+40x^44+22x^45+8x^46+1x^48+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 87.7 seconds.