The generator matrix

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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+126x^168+132x^169+276x^171+495x^172+612x^173+684x^175+771x^176+780x^177+1092x^179+489x^180+1332x^181+1704x^183+729x^184+1644x^185+1548x^187+714x^188+1116x^189+780x^191+402x^192+516x^193+60x^195+210x^196+12x^197+51x^200+30x^204+33x^208+27x^212+12x^216+3x^220+3x^224

The gray image is a linear code over GF(4) with n=244, k=7 and d=168.
This code was found by Heurico 1.16 in 1.37 seconds.