The generator matrix

 1  0  1  1  1  1  1  1  1  X  1  1  1  1 a*X  1  1  1  1 a^2*X  1  1  1  1  1  1  1  1  1  0  X  1  1  1  1  1  1  1  1  1 a*X
 0  1 a^2*X+1  a a^2*X+a^2  X a*X+1 X+a a*X+a^2  1 a*X X+1 a*X+a X+a^2  1 a^2*X  1 a^2*X+a a^2  1  0  0 a^2*X+1  a a^2*X+a^2  X a*X+1 X+a a*X+a^2  1  1 a*X X+1 a*X+a X+a^2 a^2*X  1 a^2*X+a a^2  X  1

generates a code of length 41 over F4[X]/(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.