The generator matrix

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

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+80x^45+237x^46+212x^47+362x^48+312x^49+315x^50+228x^51+207x^52+52x^53+23x^54+8x^55+5x^56+4x^57+1x^60+1x^74

The gray image is a code over GF(2) with n=392, k=11 and d=180.
This code was found by Heurico 1.16 in 0.094 seconds.