The generator matrix

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

generates a code of length 80 over F4[X]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+117x^232+384x^233+288x^234+252x^235+273x^236+660x^237+324x^238+156x^239+150x^240+276x^241+132x^242+48x^243+174x^244+144x^245+132x^246+72x^247+54x^248+84x^249+24x^250+12x^251+15x^252+84x^253+24x^254+12x^255+18x^256+48x^257+12x^258+24x^259+24x^260+48x^261+24x^262+3x^268+3x^276

The gray image is a linear code over GF(4) with n=320, k=6 and d=232.
This code was found by Heurico 1.16 in 0.156 seconds.