The generator matrix

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

generates a code of length 88 over F4[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+1800x^248+5760x^252+9264x^256+10824x^260+11220x^264+10224x^268+8838x^272+4968x^276+2124x^280+480x^284+33x^288

The gray image is a linear code over GF(4) with n=352, k=8 and d=248.
This code was found by Heurico 1.16 in 241 seconds.