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

generates a code of length 75 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 217.

Homogenous weight enumerator: w(x)=1x^0+360x^217+144x^218+48x^219+492x^220+624x^221+180x^222+96x^223+363x^224+528x^225+84x^226+12x^227+99x^228+252x^229+48x^230+12x^231+138x^232+120x^233+96x^234+78x^236+96x^237+12x^238+12x^239+3x^240+96x^241+12x^242+12x^243+36x^244+36x^245+3x^252+3x^264

The gray image is a linear code over GF(4) with n=300, k=6 and d=217.
This code was found by Heurico 1.16 in 0.203 seconds.