The generator matrix

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

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+204x^220+432x^221+204x^222+264x^223+384x^224+552x^225+156x^226+120x^227+219x^228+240x^229+72x^230+84x^231+201x^232+228x^233+72x^234+48x^235+72x^236+168x^237+24x^238+12x^239+66x^240+48x^241+36x^242+48x^243+42x^244+24x^245+12x^246+24x^248+36x^249+3x^252

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 0.125 seconds.