The generator matrix

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

generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 249.

Homogenous weight enumerator: w(x)=1x^0+192x^249+48x^252+15x^256

The gray image is a linear code over GF(4) with n=332, k=4 and d=249.
This code was found by Heurico 1.16 in 1.28 seconds.