The generator matrix

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

generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+384x^184+516x^185+576x^186+1092x^187+2529x^188+2172x^189+2244x^190+2916x^191+5802x^192+5100x^193+4188x^194+5388x^195+9960x^196+8256x^197+6636x^198+8568x^199+14970x^200+12756x^201+9768x^202+11460x^203+18924x^204+14412x^205+10764x^206+11544x^207+18768x^208+13260x^209+8760x^210+9156x^211+12396x^212+7992x^213+4644x^214+4344x^215+5064x^216+2808x^217+1464x^218+744x^219+1122x^220+288x^221+96x^222+84x^223+108x^224+24x^225+12x^226+36x^228+24x^232+3x^236+15x^240+6x^244

The gray image is a linear code over GF(4) with n=272, k=9 and d=184.
This code was found by Heurico 1.16 in 272 seconds.