The generator matrix

 1  0  0  1  1  1  2 X^2+X+2  1  1  1  1  X X+2  1  X X^2+X+2  1 X^2+2  1  1  1  1 X^2+2 X+2  1  1  1 X^2  1 X^2+X+2  1 X^2+2  1  1  2  1  1  1 X^2+2 X^2+X+2 X^2+X  2 X+2 X^2+X+2  1
 0  1  0  0 X^2+3 X^2+3  1  2  0 X^2+2  1  3  1  1 X+3 X^2+X  1 X+1  1 X^2+X+2 X^2+2 X^2+X+1 X^2+X+2  1  1 X+1 X^2+X+2 X^2+X+3 X^2+X X+2  1 X^2+X+1 X^2+2  1  0  1 X^2+X  1 X+2  1 X^2  1 X^2+X  1  1 X^2
 0  0  1 X+1 X+1 X^2 X+1  1 X^2+1  X  1  X X^2+X X+1 X+3  1 X^2 X^2+X+2  3 X+2 X^2+X+1 X^2 X^2+X+1 X^2+X  1 X^2+1 X^2+2 X^2+1  1 X^2+X  X X^2+X  1 X+2 X^2  3  0 X^2+2 X^2+3 X^2+1  1 X^2  1  0 X+3 X^2+X
 0  0  0 X^2 X^2+2  0 X^2+2 X^2  2 X^2  0 X^2+2 X^2  2 X^2+2 X^2+2  2  2 X^2+2  0  0 X^2 X^2+2  2  2  0 X^2 X^2+2  2 X^2 X^2+2  0 X^2+2  2 X^2+2 X^2  2 X^2  0  0  2  0 X^2+2 X^2+2 X^2+2 X^2

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+202x^41+816x^42+1498x^43+2123x^44+2418x^45+2690x^46+2190x^47+2061x^48+1300x^49+597x^50+262x^51+127x^52+46x^53+24x^54+14x^55+8x^56+2x^57+1x^58+4x^59

The gray image is a code over GF(2) with n=368, k=14 and d=164.
This code was found by Heurico 1.16 in 1.67 seconds.