The generator matrix

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

generates a code of length 88 over F4[X]/(X^2) who´s minimum homogenous weight is 246.

Homogenous weight enumerator: w(x)=1x^0+228x^246+576x^247+297x^248+492x^249+1272x^250+1908x^251+714x^252+996x^253+2088x^254+3348x^255+978x^256+1272x^257+3120x^258+4200x^259+897x^260+1452x^261+3900x^262+5004x^263+1284x^264+1560x^265+4020x^266+4968x^267+1245x^268+1332x^269+3492x^270+3804x^271+1011x^272+1272x^273+2136x^274+2472x^275+408x^276+612x^277+912x^278+1044x^279+177x^280+204x^281+300x^282+276x^283+60x^284+24x^285+36x^286+48x^287+33x^288+21x^292+18x^296+6x^300+9x^304+3x^308+3x^316+3x^324

The gray image is a linear code over GF(4) with n=352, k=8 and d=246.
This code was found by Heurico 1.16 in 78.5 seconds.