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

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+168x^229+492x^230+84x^232+744x^233+1092x^234+81x^236+180x^237+144x^238+27x^240+108x^241+30x^244+60x^245+228x^246+21x^248+252x^249+348x^250+9x^252+24x^253+3x^264

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 4.68 seconds.