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

generates a code of length 91 over GR(16,4) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+135x^268+54x^272+768x^273+54x^284+9x^288+3x^364

The gray image is a code over GF(4) with n=364, k=5 and d=268.
This code was found by Heurico 1.16 in 0.546 seconds.