The generator matrix

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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+126x^232+48x^234+216x^235+558x^236+300x^238+804x^239+873x^240+528x^242+780x^243+1263x^244+516x^246+1152x^247+960x^248+588x^250+1200x^251+1410x^252+468x^254+1188x^255+1113x^256+456x^258+684x^259+486x^260+156x^262+120x^263+243x^264+12x^266+36x^268+36x^272+15x^276+9x^280+15x^284+12x^288+6x^292+3x^300+3x^304

The gray image is a linear code over GF(4) with n=332, k=7 and d=232.
This code was found by Heurico 1.16 in 1.94 seconds.