The generator matrix

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

generates a code of length 87 over F4[X]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+63x^244+60x^246+288x^247+477x^248+228x^250+948x^251+918x^252+396x^254+972x^255+1173x^256+588x^258+876x^259+1290x^260+708x^262+1008x^263+1380x^264+684x^266+972x^267+1176x^268+372x^270+588x^271+408x^272+36x^274+372x^275+150x^276+120x^279+39x^280+15x^284+21x^288+18x^292+12x^296+12x^300+6x^304+3x^308+3x^316+3x^320

The gray image is a linear code over GF(4) with n=348, k=7 and d=244.
This code was found by Heurico 1.16 in 2.05 seconds.