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

generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+93x^236+147x^240+48x^243+165x^244+432x^247+141x^248+1296x^251+120x^252+1296x^255+117x^256+54x^260+45x^264+36x^268+18x^272+24x^276+9x^280+15x^284+15x^288+9x^292+3x^296+6x^300+3x^308+3x^324

The gray image is a linear code over GF(4) with n=336, k=6 and d=236.
This code was found by Heurico 1.16 in 0.336 seconds.