The generator matrix

 1  0  0  1  1  1  1  1  1  1  X  1  1  1  1  1 a*X  1  1  1  1  0  X  1  1  1  1  1  1 a^2*X  1
 0  1  0 a^2*X a*X  X  1 a^2*X+1  a a^2*X+a  1 X+1 a^2*X+a^2 a*X+a a*X+a^2 a^2  1  1 a^2*X+a a*X+a^2 X+a  1  1 a^2*X X+a  X a*X X+a^2  a  X a^2
 0  0  1  1  a a^2 X+a^2 X+a  X X+1 a^2*X+a a*X a*X+a^2  a a^2*X+a a^2*X+1  1 a^2*X+1 a*X+a^2 a^2*X a^2*X+a a^2  0 X+1 a^2*X+a^2 X+1 a^2*X+a^2 a^2*X+1 X+a  1 a^2*X+a

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+228x^86+240x^87+321x^88+168x^89+528x^90+432x^91+318x^92+96x^93+336x^94+144x^95+171x^96+72x^97+288x^98+336x^99+210x^100+48x^101+156x^102+3x^104

The gray image is a linear code over GF(4) with n=124, k=6 and d=86.
This code was found by Heurico 1.16 in 0.032 seconds.