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

generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+225x^244+327x^248+465x^252+48x^253+387x^256+432x^257+420x^260+1632x^261+390x^264+3552x^265+285x^268+4464x^269+315x^272+2160x^273+261x^276+231x^280+198x^284+183x^288+135x^292+105x^296+93x^300+30x^304+27x^308+15x^312+3x^332

The gray image is a linear code over GF(4) with n=356, k=7 and d=244.
This code was found by Heurico 1.16 in 19.6 seconds.