The generator matrix

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

generates a code of length 88 over F4[X]/(X^2) who´s minimum homogenous weight is 247.

Homogenous weight enumerator: w(x)=1x^0+432x^247+429x^248+456x^249+876x^250+1704x^251+1455x^252+1788x^253+1620x^254+2700x^255+1932x^256+1908x^257+1968x^258+3768x^259+2406x^260+2376x^261+2592x^262+4140x^263+2394x^264+2136x^265+2388x^266+4032x^267+2475x^268+2100x^269+2004x^270+2796x^271+1962x^272+1752x^273+1428x^274+2052x^275+1236x^276+948x^277+708x^278+1104x^279+492x^280+324x^281+204x^282+300x^283+60x^284+36x^285+36x^286+12x^287+3x^288+3x^296

The gray image is a linear code over GF(4) with n=352, k=8 and d=247.
This code was found by Heurico 1.16 in 28.3 seconds.