The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2
 0  2  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  2  0  2
 0  0  2  0  0  0  0  2  0  2  2  0  0  2  2  0  2  2  2  2  2  2  0  0  2  2  0
 0  0  0  2  0  0  0  2  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  2  0  2
 0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0
 0  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  0  2  2  2  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+21x^24+32x^26+67x^28+6x^32+1x^52

The gray image is a code over GF(2) with n=54, k=7 and d=24.
This code was found by Heurico 1.16 in 0.00504 seconds.