The generator matrix

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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+660x^81+1164x^82+636x^83+93x^84+2544x^85+3360x^86+1320x^87+189x^88+5292x^89+6168x^90+2316x^91+342x^92+8916x^93+9024x^94+2964x^95+231x^96+8112x^97+6396x^98+1704x^99+120x^100+2124x^101+1536x^102+276x^103+24x^104+18x^108+3x^116+3x^120

The gray image is a linear code over GF(4) with n=124, k=8 and d=81.
This code was found by Heurico 1.16 in 413 seconds.