The generator matrix

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

generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+420x^265+708x^266+756x^267+789x^268+2136x^269+1356x^270+1404x^271+1410x^272+2688x^273+2280x^274+2088x^275+1860x^276+3684x^277+2664x^278+2112x^279+2049x^280+3672x^281+3096x^282+2256x^283+1839x^284+3456x^285+2580x^286+2208x^287+1659x^288+3348x^289+2088x^290+1668x^291+1182x^292+2160x^293+1320x^294+876x^295+669x^296+1128x^297+636x^298+384x^299+282x^300+324x^301+144x^302+72x^303+36x^304+24x^305+24x^306

The gray image is a linear code over GF(4) with n=376, k=8 and d=265.
This code was found by Heurico 1.16 in 32.2 seconds.