The generator matrix

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

generates a code of length 76 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+480x^220+1815x^224+432x^228+588x^232+228x^236+465x^240+60x^244+24x^248+3x^272

The gray image is a linear code over GF(4) with n=304, k=6 and d=220.
This code was found by Heurico 1.16 in 0.165 seconds.