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

generates a code of length 88 over F4[X]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+666x^252+576x^253+432x^254+288x^255+1173x^256+924x^257+660x^258+312x^259+1491x^260+840x^261+636x^262+276x^263+1221x^264+684x^265+480x^266+288x^267+945x^268+672x^269+360x^270+204x^271+672x^272+444x^273+288x^274+108x^275+552x^276+240x^277+120x^278+48x^279+312x^280+156x^281+60x^282+12x^283+111x^284+72x^285+36x^286+18x^288+3x^292+3x^296

The gray image is a linear code over GF(4) with n=352, k=7 and d=252.
This code was found by Heurico 1.16 in 1.53 seconds.