The generator matrix

 1  0  0  0  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  1 aX (a+1)X  X  1  1 (a+1)X  1  1  1  1  1  1  1  1  1  1 aX  1  1 aX  1  1  1 (a+1)X  1  1 (a+1)X (a+1)X  1  1  1  X aX  1  1  1  1  1  1  X  1  1  X  1 (a+1)X  1  1  1  1 aX  1  1  0  1  1  1  1  1  1 aX aX  1  1  1
 0  1  0  0  0  0 (a+1)X (a+1)X (a+1)X aX  1 aX+1  1 (a+1)X+1 X+a+1  1 aX+a+1 X+1 aX+1  1  1  1  1  1  X X+a+1  1  X aX+1 aX+a+1 (a+1)X+a+1 X+a+1 (a+1)X+a aX+1 (a+1)X+a+1 (a+1)X+a  X  1 X+a X+a+1  1 (a+1)X+a (a+1)X+a+1 (a+1)X+1 aX  X  0  1  1 (a+1)X+a+1 a+1 (a+1)X  1  X X+a X+a a+1  0 X+a+1 aX+a  1 X+a (a+1)X+a  1  a (a+1)X  1 X+a+1 aX (a+1)X+a  1 X+1 aX+1  1  X X+1 a+1 X+1 X+a aX+a+1  1  1 X+1 aX+a+1 (a+1)X+a+1
 0  0  1  0  0  X  0 (a+1)X+1  a (a+1)X+1 (a+1)X+1  1  X aX+1  X aX (a+1)X+1 aX+a aX+a+1 X+a (a+1)X+a+1 X+a+1 aX+a  0 aX+a (a+1)X+a X+1 aX+a+1 aX+a aX+1 aX (a+1)X  a (a+1)X a+1 X+1 aX+a X+1 a+1 (a+1)X+1  X aX+a (a+1)X+a+1 a+1  1 aX+a+1  a a+1 (a+1)X+a+1 a+1 X+1 X+a X+a+1  1 aX+1 (a+1)X+a+1 aX+a+1 aX+a X+a aX a+1 X+a  X aX (a+1)X  1  0  X (a+1)X+a+1  X (a+1)X (a+1)X (a+1)X+a (a+1)X+1 aX+1 (a+1)X+a (a+1)X+a+1 aX+a+1 aX+a+1  1 (a+1)X+a X+a+1 X+1 X+a  0
 0  0  0  1  1 (a+1)X+a a+1 a+1 X+a+1  a (a+1)X+a+1  X aX+a+1 (a+1)X+1  1 (a+1)X+a aX+a X+a+1 (a+1)X+1 aX+1  a (a+1)X+1  X a+1 (a+1)X+1 aX+a aX+a (a+1)X+a+1 X+a aX+1 (a+1)X+a+1 (a+1)X X+a+1 (a+1)X (a+1)X+a  a aX+a  X X+a+1 a+1 aX+1  X aX+1 aX (a+1)X+a (a+1)X+a  X aX+a+1 X+a X+a+1  X  0 aX X+a+1  X (a+1)X+a  X (a+1)X+a+1 X+1 (a+1)X aX+a+1 a+1 (a+1)X+a+1 (a+1)X+1  1 aX X+a (a+1)X+1 (a+1)X (a+1)X+a  0  1 X+a+1  1 aX+a+1 (a+1)X+1 X+1  1 X+1 aX+a aX+a  a aX+a+1 (a+1)X aX+a
 0  0  0  0 (a+1)X  X aX  0  X (a+1)X  0  0  0 (a+1)X aX (a+1)X aX aX aX  X  0 (a+1)X (a+1)X aX aX  X  0 (a+1)X  X (a+1)X aX (a+1)X aX  X  X  0  0 aX aX (a+1)X  X (a+1)X  X (a+1)X  0  X  0 aX  0  0  X  X (a+1)X  X  0  X (a+1)X aX (a+1)X  X  X  0 (a+1)X aX  X (a+1)X aX  0 aX  0 (a+1)X aX (a+1)X (a+1)X (a+1)X aX aX  X aX  0  0 aX  X aX  X

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 234.

Homogenous weight enumerator: w(x)=1x^0+456x^234+852x^235+933x^236+1044x^237+2352x^238+2700x^239+2568x^240+2616x^241+4680x^242+5340x^243+4866x^244+4728x^245+8208x^246+8568x^247+7275x^248+6384x^249+12072x^250+11796x^251+9720x^252+8784x^253+14232x^254+13020x^255+12027x^256+9636x^257+15372x^258+13716x^259+10647x^260+8316x^261+12432x^262+9768x^263+7218x^264+5016x^265+7032x^266+5592x^267+3069x^268+2052x^269+2376x^270+1920x^271+834x^272+540x^273+612x^274+432x^275+159x^276+36x^277+48x^278+24x^279+21x^280+18x^284+9x^288+6x^292+12x^296+6x^300+3x^304

The gray image is a linear code over GF(4) with n=340, k=9 and d=234.
This code was found by Heurico 1.16 in 673 seconds.