The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  X X+2  1  1  X  1  1 X+2 X+2  0  X  1  1  0  1  X  1  2  1  X  1  X  2  1  1  X  1
 0  1  0  2  3  1  1  0  3  1  2  1  1 X+2  X  0  X X+3  1 X+2 X+1  1 X+2  X  0  2  1  1 X+2  1  0  1 X+2  1  X  2  0 X+3 X+1  1  X
 0  0  1 X+3 X+1  2 X+1 X+2  3  3  1  X X+2  1  1  1  1  X  X X+1  0  2  1  1  1 X+1  0  2  3  2  1  X X+2 X+3 X+1  1  1 X+3  1 X+2 X+2

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+48x^38+134x^39+77x^40+72x^41+58x^42+46x^43+20x^44+20x^45+5x^46+16x^47+13x^48+1x^50+1x^60

The gray image is a code over GF(2) with n=164, k=9 and d=76.
This code was found by Heurico 1.13 in 0.015 seconds.