The generator matrix

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

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+210x^45+485x^46+520x^47+592x^48+576x^49+706x^50+374x^51+320x^52+180x^53+52x^54+44x^55+13x^56+8x^57+3x^58+6x^59+2x^60+2x^61+1x^62+1x^66

The gray image is a code over GF(2) with n=392, k=12 and d=180.
This code was found by Heurico 1.16 in 81.8 seconds.