The generator matrix

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

generates a code of length 71 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+57x^196+96x^198+132x^199+489x^200+264x^202+720x^203+909x^204+348x^206+852x^207+1098x^208+552x^210+1284x^211+1395x^212+744x^214+1356x^215+1314x^216+552x^218+1080x^219+1164x^220+444x^222+636x^223+540x^224+72x^226+84x^227+84x^228+27x^232+18x^236+24x^240+12x^244+18x^248+9x^252+9x^256

The gray image is a linear code over GF(4) with n=284, k=7 and d=196.
This code was found by Heurico 1.16 in 1.61 seconds.