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

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+624x^81+1296x^82+624x^83+102x^84+2568x^85+3360x^86+1176x^87+171x^88+5232x^89+5844x^90+2520x^91+339x^92+9024x^93+9252x^94+3048x^95+255x^96+8160x^97+6252x^98+1560x^99+111x^100+2040x^101+1644x^102+288x^103+18x^104+21x^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 58.6 seconds.