The generator matrix

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

generates a code of length 75 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 212.

Homogenous weight enumerator: w(x)=1x^0+177x^212+12x^213+273x^216+144x^217+96x^220+648x^221+15x^224+1296x^225+177x^228+972x^229+108x^232+30x^236+57x^244+42x^248+9x^252+21x^260+6x^264+6x^268+3x^280+3x^284

The gray image is a linear code over GF(4) with n=300, k=6 and d=212.
This code was found by Heurico 1.16 in 44.5 seconds.