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  2  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  1 a+3  a a+2
 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+3 3a 3a+1 3a+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 2a+2 3a+2 3a+2 3a+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+516x^89+360x^90+540x^91+1044x^92+2028x^93+1308x^94+1812x^95+2268x^96+3672x^97+2760x^98+2940x^99+3651x^100+6060x^101+4176x^102+4572x^103+4599x^104+6936x^105+3984x^106+3192x^107+2682x^108+3384x^109+1236x^110+768x^111+582x^112+444x^113+15x^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 8.43 seconds.