The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^27+159x^28+188x^29+252x^30+252x^31+289x^32+338x^33+319x^34+336x^35+336x^36+330x^37+316x^38+300x^39+232x^40+150x^41+95x^42+50x^43+37x^44+18x^45+7x^46+8x^47+2x^48+2x^50+1x^54

The gray image is a code over GF(2) with n=70, k=12 and d=27.
This code was found by Heurico 1.10 in 0.484 seconds.