The generator matrix

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

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+192x^188+660x^189+336x^190+780x^191+1491x^192+2304x^193+1080x^194+1596x^195+2535x^196+3420x^197+1488x^198+1944x^199+3324x^200+4716x^201+1584x^202+2220x^203+4044x^204+4752x^205+1800x^206+2664x^207+3738x^208+4152x^209+1668x^210+1680x^211+2706x^212+3168x^213+924x^214+1092x^215+1188x^216+1152x^217+324x^218+312x^219+216x^220+240x^221+12x^222+18x^224+12x^225+3x^228

The gray image is a linear code over GF(4) with n=272, k=8 and d=188.
This code was found by Heurico 1.16 in 21.4 seconds.