The generator matrix

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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+252x^252+216x^253+264x^254+819x^256+780x^257+408x^258+1164x^260+996x^261+444x^262+1086x^264+1140x^265+516x^266+1215x^268+984x^269+492x^270+1224x^272+1044x^273+624x^274+873x^276+756x^277+228x^278+360x^280+204x^281+84x^282+48x^284+24x^285+12x^286+33x^288+24x^292+24x^296+12x^300+9x^304+9x^308+12x^312+3x^316

The gray image is a linear code over GF(4) with n=356, k=7 and d=252.
This code was found by Heurico 1.16 in 2.47 seconds.