The generator matrix

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

generates a code of length 86 over F4[X]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+171x^236+396x^237+372x^238+876x^239+2226x^240+1836x^241+2016x^242+2868x^243+4479x^244+4068x^245+4164x^246+4800x^247+7470x^248+6348x^249+6468x^250+7608x^251+11229x^252+8532x^253+8712x^254+10140x^255+14766x^256+11340x^257+10140x^258+12384x^259+15918x^260+11160x^261+10452x^262+10764x^263+13632x^264+9744x^265+7176x^266+7560x^267+9621x^268+5316x^269+4140x^270+3480x^271+3303x^272+2064x^273+1452x^274+876x^275+948x^276+564x^277+192x^278+84x^279+117x^280+60x^281+12x^282+45x^284+12x^285+12x^288+12x^292+9x^296+6x^300+3x^308

The gray image is a linear code over GF(4) with n=344, k=9 and d=236.
This code was found by Heurico 1.16 in 380 seconds.