The generator matrix

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

generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+63x^188+60x^189+60x^190+348x^191+198x^192+336x^193+372x^194+1008x^195+165x^196+372x^197+444x^198+1512x^199+120x^200+564x^201+600x^202+2100x^203+99x^204+672x^205+660x^206+2124x^207+93x^208+504x^209+612x^210+1656x^211+78x^212+420x^213+276x^214+432x^215+69x^216+132x^217+48x^218+36x^219+18x^220+12x^221+30x^224+36x^228+21x^232+12x^236+6x^240+9x^244+6x^248

The gray image is a linear code over GF(4) with n=272, k=7 and d=188.
This code was found by Heurico 1.16 in 1.55 seconds.