The generator matrix

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

generates a code of length 80 over F4[X]/(X^2) who´s minimum homogenous weight is 233.

Homogenous weight enumerator: w(x)=1x^0+1056x^233+576x^236+576x^237+240x^240+672x^241+480x^249+192x^252+192x^253+15x^256+96x^257

The gray image is a linear code over GF(4) with n=320, k=6 and d=233.
This code was found by Heurico 1.16 in 54.2 seconds.