The generator matrix

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

generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+825x^72+576x^74+2493x^76+1152x^78+3168x^80+1728x^82+3537x^84+1152x^86+1716x^88+15x^92+15x^96+3x^100+3x^104

The gray image is a code over GF(4) with n=108, k=7 and d=72.
This code was found by Heurico 1.16 in 0.4 seconds.