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

generates a code of length 80 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+261x^228+1212x^229+801x^232+2496x^233+801x^236+2364x^237+660x^240+2292x^241+636x^244+1596x^245+369x^248+1200x^249+429x^252+684x^253+105x^256+348x^257+33x^260+96x^261

The gray image is a linear code over GF(4) with n=320, k=7 and d=228.
This code was found by Heurico 1.16 in 1.52 seconds.