The generator matrix

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

generates a code of length 34 over GR(16,4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+396x^89+264x^90+588x^91+1131x^92+2328x^93+1308x^94+1416x^95+2361x^96+4176x^97+2328x^98+2928x^99+4107x^100+6168x^101+3744x^102+3624x^103+5265x^104+7380x^105+3552x^106+3012x^107+3009x^108+3600x^109+1092x^110+720x^111+495x^112+528x^113+9x^116+3x^120+3x^128

The gray image is a code over GF(4) with n=136, k=8 and d=89.
This code was found by Heurico 1.16 in 8.08 seconds.