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

generates a code of length 81 over GR(16,4) who´s minimum homogenous weight is 243.

Homogenous weight enumerator: w(x)=1x^0+192x^243+24x^244+36x^248+3x^256

The gray image is a code over GF(4) with n=324, k=4 and d=243.
This code was found by Heurico 1.16 in 0.297 seconds.