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

generates a code of length 92 over F4[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+174x^260+144x^262+456x^263+690x^264+396x^266+852x^267+1041x^268+468x^270+1020x^271+1089x^272+456x^274+996x^275+1245x^276+516x^278+1020x^279+1299x^280+684x^282+1020x^283+900x^284+300x^286+564x^287+492x^288+96x^290+204x^291+93x^292+12x^294+12x^295+51x^296+15x^300+21x^304+12x^308+6x^312+18x^316+15x^320+6x^324

The gray image is a linear code over GF(4) with n=368, k=7 and d=260.
This code was found by Heurico 1.16 in 2.21 seconds.