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

generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 230.

Homogenous weight enumerator: w(x)=1x^0+720x^230+474x^232+960x^234+180x^236+696x^238+171x^240+252x^242+96x^244+180x^246+48x^248+84x^250+12x^252+132x^254+36x^256+48x^258+3x^264+3x^280

The gray image is a linear code over GF(4) with n=316, k=6 and d=230.
This code was found by Heurico 1.16 in 33.4 seconds.