The generator matrix

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

generates a code of length 84 over F4[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+306x^240+1344x^241+726x^244+2556x^245+870x^248+2304x^249+660x^252+1860x^253+531x^256+1752x^257+492x^260+1248x^261+321x^264+828x^265+135x^268+336x^269+48x^272+60x^273+3x^280+3x^284

The gray image is a linear code over GF(4) with n=336, k=7 and d=240.
This code was found by Heurico 1.16 in 1.38 seconds.