The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+123x^24+74x^28+51x^32+6x^36+1x^40

The gray image is a code over GF(2) with n=54, k=8 and d=24.
This code was found by Heurico 1.16 in 1.52 seconds.