The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2a+2  1  1  1  1  1  1  1  1  0 2a+2 2a  1  1  1  1
 0  1  0 2a+2 2a  2  1 3a+2 2a+3  a 2a+1  1 a+2 3a+1 3a+3  3 a+1 a+3 3a+2 a+2  1  1  1 2a+1  a 2a+2 3a
 0  0  1  1  a 3a+3 3a+1 a+1 a+2  2  3  1 3a+2 2a+2 2a+1 2a a+3 3a 2a+1  1  a 3a+3 a+1 2a+3 a+1  3  2

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+468x^75+180x^76+336x^77+240x^78+900x^79+189x^80+192x^81+252x^83+180x^84+144x^85+144x^86+684x^87+90x^88+96x^89

The gray image is a code over GF(4) with n=108, k=6 and d=75.
This code was found by Heurico 1.16 in 0.016 seconds.