The generator matrix

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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 237.

Homogenous weight enumerator: w(x)=1x^0+576x^237+780x^238+360x^239+42x^240+1188x^241+1344x^242+480x^243+36x^244+1212x^245+1344x^246+420x^247+63x^248+1284x^249+1188x^250+396x^251+60x^252+1176x^253+912x^254+228x^255+18x^256+672x^257+624x^258+240x^259+15x^260+480x^261+456x^262+132x^263+9x^264+264x^265+204x^266+36x^267+6x^268+60x^269+60x^270+12x^271+3x^272+3x^276

The gray image is a linear code over GF(4) with n=332, k=7 and d=237.
This code was found by Heurico 1.16 in 28.2 seconds.