The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+22x^40+19x^42+116x^44+724x^46+112x^48+10x^50+4x^52+4x^54+11x^58+1x^80

The gray image is a code over GF(2) with n=368, k=10 and d=160.
This code was found by Heurico 1.16 in 0.078 seconds.