The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+54x^41+109x^42+192x^43+234x^44+272x^45+361x^46+332x^47+235x^48+104x^49+47x^50+36x^51+18x^52+16x^53+11x^54+12x^55+7x^56+2x^57+4x^59+1x^72

The gray image is a code over GF(2) with n=368, k=11 and d=164.
This code was found by Heurico 1.16 in 1.58 seconds.