The generator matrix

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

generates a code of length 32 over GR(16,4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+468x^86+432x^87+183x^88+1644x^90+1284x^91+213x^92+2352x^94+1620x^95+231x^96+2592x^98+1932x^99+237x^100+1884x^102+876x^103+126x^104+276x^106+27x^108+3x^116+3x^120

The gray image is a code over GF(4) with n=128, k=7 and d=86.
This code was found by Heurico 1.16 in 0.654 seconds.