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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+144x^188+12x^189+207x^192+144x^193+201x^196+648x^197+135x^200+1296x^201+78x^204+972x^205+54x^208+24x^212+57x^216+36x^220+24x^224+27x^228+12x^232+9x^236+6x^244+6x^248+3x^252

The gray image is a linear code over GF(4) with n=268, k=6 and d=188.
This code was found by Heurico 1.16 in 49.2 seconds.