The generator matrix

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

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+180x^232+384x^236+402x^240+96x^241+432x^244+336x^245+426x^248+1536x^249+294x^252+3936x^253+375x^256+4128x^257+330x^260+2256x^261+279x^264+234x^268+213x^272+189x^276+114x^280+84x^284+66x^288+57x^292+21x^296+9x^300+3x^304+3x^316

The gray image is a linear code over GF(4) with n=340, k=7 and d=232.
This code was found by Heurico 1.16 in 4.71 seconds.