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

generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 229.

Homogenous weight enumerator: w(x)=1x^0+264x^229+516x^230+117x^232+456x^233+732x^234+66x^236+372x^237+528x^238+15x^240+192x^241+180x^242+96x^245+144x^246+27x^248+72x^249+120x^250+24x^252+36x^253+60x^254+48x^257+24x^258+6x^268

The gray image is a linear code over GF(4) with n=316, k=6 and d=229.
This code was found by Heurico 1.16 in 0.141 seconds.