The generator matrix

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

generates a code of length 34 over GR(16,4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+123x^88+432x^91+267x^92+1344x^95+516x^96+2928x^99+987x^100+4176x^103+1368x^104+2976x^107+606x^108+432x^111+93x^112+75x^116+27x^120+33x^124

The gray image is a code over GF(4) with n=136, k=7 and d=88.
This code was found by Heurico 1.16 in 0.663 seconds.