The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+93x^24+42x^26+71x^28+14x^30+20x^32+6x^34+5x^36+2x^38+2x^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 0.00506 seconds.