The generator matrix

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

generates a code of length 66 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+216x^182+348x^183+573x^184+804x^185+1332x^186+1464x^187+1437x^188+2160x^189+2712x^190+2340x^191+2535x^192+2556x^193+3300x^194+2772x^195+2802x^196+2988x^197+4272x^198+2892x^199+2964x^200+2904x^201+4164x^202+2616x^203+2520x^204+2136x^205+2724x^206+2100x^207+1539x^208+1308x^209+1032x^210+732x^211+414x^212+492x^213+204x^214+96x^215+57x^216+12x^217+12x^218+3x^220+3x^224

The gray image is a linear code over GF(4) with n=264, k=8 and d=182.
This code was found by Heurico 1.16 in 18.4 seconds.