The generator matrix

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

generates a code of length 29 over GR(16,4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+78x^68+309x^72+417x^76+192x^78+468x^80+1728x^82+594x^84+5184x^86+591x^88+5184x^90+594x^92+552x^96+300x^100+156x^104+33x^108+3x^112

The gray image is a code over GF(4) with n=116, k=7 and d=68.
This code was found by Heurico 1.16 in 1.01 seconds.