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  X  1  X  1  1  1  1  1  1  2  1  1  0  1  X  2  X  2  X  X
 0 2X+2  0 2X+2  0 2X+2  0  2 2X 2X+2  0 2X+2 2X+2  0 2X  2  0 2X 2X+2  2 2X+2  2  0  0  0 2X 2X+2 2X+2 2X+2 2X+2 2X+2  2  2 2X+2  2 2X+2 2X+2  2  2  2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2
 0  0 2X  0  0  0  0  0 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0
 0  0  0 2X  0  0  0 2X  0  0  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X 2X  0 2X  0 2X  0 2X 2X  0 2X
 0  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X  0  0 2X 2X 2X
 0  0  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X 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+68x^40+104x^42+64x^43+252x^44+448x^45+176x^46+448x^47+269x^48+64x^49+104x^50+32x^52+11x^56+4x^60+2x^64+1x^72

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 0.141 seconds.