The generator matrix

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

generates a code of length 82 over GR(16,4) who´s minimum homogenous weight is 234.

Homogenous weight enumerator: w(x)=1x^0+636x^234+636x^235+129x^236+1680x^238+1128x^239+216x^240+1884x^242+1452x^243+219x^244+1536x^246+948x^247+204x^248+1440x^250+756x^251+96x^252+936x^254+648x^255+39x^256+660x^258+348x^259+78x^260+360x^262+156x^263+36x^264+84x^266+72x^267+3x^268+3x^276

The gray image is a code over GF(4) with n=328, k=7 and d=234.
This code was found by Heurico 1.16 in 8.59 seconds.