The generator matrix

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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+219x^248+180x^249+72x^250+348x^251+1803x^252+696x^253+372x^254+1116x^255+3489x^256+1152x^257+792x^258+1644x^259+4578x^260+1812x^261+972x^262+1836x^263+5517x^264+2448x^265+1092x^266+2268x^267+6309x^268+2040x^269+1248x^270+2124x^271+5835x^272+1728x^273+864x^274+1524x^275+3825x^276+1524x^277+444x^278+1044x^279+2136x^280+540x^281+252x^282+360x^283+837x^284+168x^285+36x^286+24x^287+168x^288+48x^292+15x^296+18x^300+6x^304+3x^308+3x^312+3x^316+3x^320

The gray image is a linear code over GF(4) with n=356, k=8 and d=248.
This code was found by Heurico 1.16 in 27.6 seconds.