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

generates a code of length 77 over F4[X]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+90x^216+219x^220+48x^222+159x^224+432x^226+135x^228+1296x^230+87x^232+1296x^234+84x^236+69x^240+36x^244+24x^248+30x^252+39x^256+15x^260+12x^264+9x^268+6x^272+6x^280+3x^296

The gray image is a linear code over GF(4) with n=308, k=6 and d=216.
This code was found by Heurico 1.16 in 0.291 seconds.