The generator matrix

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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+534x^164+432x^165+768x^166+1512x^167+2541x^168+2148x^169+2172x^170+4176x^171+6330x^172+4656x^173+5064x^174+7452x^175+11535x^176+7344x^177+7716x^178+11412x^179+16713x^180+11448x^181+10452x^182+15048x^183+20703x^184+13248x^185+10896x^186+15276x^187+18201x^188+10128x^189+8064x^190+9036x^191+10215x^192+4656x^193+3396x^194+3180x^195+3033x^196+1176x^197+612x^198+456x^199+216x^200+60x^201+12x^202+36x^203+51x^204+15x^208+15x^212+6x^216+3x^228

The gray image is a linear code over GF(4) with n=244, k=9 and d=164.
This code was found by Heurico 1.16 in 240 seconds.