The generator matrix

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

generates a code of length 93 over F4[X]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+153x^260+240x^261+84x^262+684x^263+1215x^264+1080x^265+216x^266+1980x^267+2631x^268+1680x^269+336x^270+2748x^271+3606x^272+2220x^273+528x^274+3528x^275+4014x^276+2124x^277+552x^278+3564x^279+4458x^280+2904x^281+468x^282+3672x^283+4155x^284+2448x^285+444x^286+2940x^287+3114x^288+1404x^289+264x^290+1608x^291+1455x^292+924x^293+108x^294+600x^295+594x^296+264x^297+60x^298+156x^299+96x^300+72x^301+12x^302+24x^303+60x^304+12x^308+6x^312+12x^316+9x^320+6x^328+3x^344

The gray image is a linear code over GF(4) with n=372, k=8 and d=260.
This code was found by Heurico 1.16 in 29.1 seconds.