The generator matrix

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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+282x^80+768x^81+432x^82+432x^83+1491x^84+2820x^85+996x^86+1056x^87+3045x^88+5040x^89+2064x^90+2880x^91+6006x^92+8664x^93+3096x^94+3168x^95+5877x^96+7728x^97+2208x^98+1680x^99+2553x^100+2628x^101+420x^102+93x^104+60x^108+30x^112+18x^116

The gray image is a linear code over GF(4) with n=124, k=8 and d=80.
This code was found by Heurico 1.16 in 16.9 seconds.