The generator matrix

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

generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+165x^232+201x^236+144x^238+138x^240+720x^242+123x^244+1200x^246+87x^248+1008x^250+57x^252+66x^256+45x^260+27x^264+30x^268+39x^272+12x^276+15x^280+12x^284+3x^296+3x^312

The gray image is a linear code over GF(4) with n=328, k=6 and d=232.
This code was found by Heurico 1.16 in 0.502 seconds.