The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  X  1  1  0  1  1  1 a*X  1  1  1  1  1  1  1
 0  1  1  a a^2  0 a^2*X+1 a^2*X+a^2  a  1  0 a^2*X+1  a  1 a^2*X+a^2 X+a  1 a^2*X+1 a^2*X+a^2  1  a  0 a^2*X+a  1 a^2*X+a^2 a^2 a*X+1 X+a a*X+1 a*X+a^2  X
 0  0 a^2*X  0  0  0  X  X  X  X  X  X a^2*X a^2*X a*X a^2*X a^2*X  0 a*X a*X a^2*X a^2*X a^2*X a*X a^2*X a^2*X  X a*X  X  X  0
 0  0  0  X  0  X a^2*X  0  X a^2*X  X  0 a*X a^2*X  0  0  X a*X  X  X a^2*X a*X  X a^2*X  X  X  X  0  0  0  X
 0  0  0  0 a^2*X a^2*X  X a^2*X a*X  0 a^2*X  X  X a*X  X  X  X  0  0 a*X a^2*X  0 a^2*X  X  0  X  X  0 a^2*X  0 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+135x^80+48x^82+288x^83+678x^84+288x^86+720x^87+1074x^88+768x^90+1872x^91+2112x^92+1248x^94+2160x^95+2079x^96+720x^98+1104x^99+882x^100+90x^104+60x^108+45x^112+12x^116

The gray image is a linear code over GF(4) with n=124, k=7 and d=80.
This code was found by Heurico 1.16 in 0.593 seconds.