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

generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 237.

Homogenous weight enumerator: w(x)=1x^0+504x^237+720x^238+384x^239+39x^240+1356x^241+1248x^242+444x^243+48x^244+1200x^245+1476x^246+480x^247+54x^248+1248x^249+1332x^250+360x^251+60x^252+1044x^253+804x^254+240x^255+24x^256+792x^257+672x^258+180x^259+3x^260+372x^261+420x^262+120x^263+15x^264+300x^265+204x^266+72x^267+6x^268+96x^269+36x^270+24x^271+3x^276+3x^280

The gray image is a linear code over GF(4) with n=332, k=7 and d=237.
This code was found by Heurico 1.16 in 19.1 seconds.