The generator matrix

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

generates a code of length 75 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 213.

Homogenous weight enumerator: w(x)=1x^0+432x^213+540x^214+276x^215+345x^216+1236x^217+1152x^218+540x^219+336x^220+1272x^221+936x^222+444x^223+312x^224+1404x^225+924x^226+432x^227+351x^228+1176x^229+780x^230+300x^231+207x^232+672x^233+540x^234+108x^235+198x^236+396x^237+372x^238+132x^239+39x^240+288x^241+120x^242+72x^243+3x^244+36x^245+12x^246

The gray image is a linear code over GF(4) with n=300, k=7 and d=213.
This code was found by Heurico 1.16 in 1.42 seconds.