The generator matrix

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

generates a code of length 79 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+684x^225+264x^226+396x^227+195x^228+1524x^229+636x^230+684x^231+195x^232+2076x^233+756x^234+564x^235+228x^236+1524x^237+432x^238+480x^239+147x^240+1296x^241+384x^242+432x^243+102x^244+900x^245+276x^246+408x^247+102x^248+852x^249+204x^250+96x^251+48x^252+276x^253+96x^254+12x^255+84x^257+24x^258+3x^260+3x^280

The gray image is a linear code over GF(4) with n=316, k=7 and d=225.
This code was found by Heurico 1.16 in 1.38 seconds.