The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+4x^26+16x^27+6x^28+2x^30+1x^32+2x^34

The gray image is a code over GF(2) with n=54, k=5 and d=26.
This code was found by Heurico 1.16 in 0.00176 seconds.