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

generates a code of length 81 over F4[X]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+117x^228+183x^232+48x^234+168x^236+432x^238+135x^240+1296x^242+108x^244+1296x^246+63x^248+51x^252+39x^256+39x^260+33x^264+21x^268+24x^272+18x^276+12x^280+6x^284+3x^288+3x^312

The gray image is a linear code over GF(4) with n=324, k=6 and d=228.
This code was found by Heurico 1.16 in 0.317 seconds.