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

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+113x^40+120x^44+1536x^46+226x^48+8x^52+43x^56+1x^80

The gray image is a code over GF(2) with n=368, k=11 and d=160.
This code was found by Heurico 1.16 in 8.09 seconds.