The generator matrix

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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+24x^121+36x^122+144x^123+3x^124+24x^125+12x^126+9x^132+3x^136

The gray image is a linear code over GF(4) with n=164, k=4 and d=121.
This code was found by Heurico 1.16 in 0.031 seconds.