The generator matrix

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

generates a code of length 31 over F4[X]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+504x^83+303x^84+2304x^87+930x^88+3000x^91+960x^92+3816x^95+1287x^96+2352x^99+558x^100+312x^103+54x^104+3x^116

The gray image is a linear code over GF(4) with n=124, k=7 and d=83.
This code was found by Heurico 1.16 in 0.538 seconds.