The generator matrix

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

generates a code of length 92 over F4[X]/(X^2) who´s minimum homogenous weight is 257.

Homogenous weight enumerator: w(x)=1x^0+132x^257+228x^258+336x^259+510x^260+1056x^261+852x^262+1056x^263+1218x^264+2064x^265+1728x^266+1920x^267+1884x^268+2964x^269+2340x^270+2244x^271+2028x^272+3648x^273+2496x^274+2748x^275+2181x^276+3564x^277+2436x^278+2748x^279+2316x^280+3492x^281+2688x^282+2292x^283+1515x^284+2616x^285+1500x^286+1116x^287+966x^288+1380x^289+876x^290+756x^291+447x^292+540x^293+168x^294+132x^295+168x^296+36x^297+48x^298+12x^299+9x^300+12x^301+21x^304+15x^308+9x^312+6x^316+3x^320+9x^324+3x^328+3x^336

The gray image is a linear code over GF(4) with n=368, k=8 and d=257.
This code was found by Heurico 1.16 in 28.4 seconds.