The generator matrix

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

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+23x^38+24x^39+75x^40+20x^41+67x^42+16x^43+20x^44+4x^45+5x^46+1x^74

The gray image is a code over GF(2) with n=164, k=8 and d=76.
This code was found by Heurico 1.16 in 0.0298 seconds.