The generator matrix

 1  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  1  X  1  1  1  X  X  1  1  1  1  0  1  1  X  1  X  0  1  1  2  X
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2+2 X^2 X^2+X X^2+X  0  2 X+2  X X^2  X X^2+X+2  X  0 X^2+X+2  2 X^2+X+2 X^2+X+2 X^2+X+2 X^2  X X+2 X+2 X^2+2 X^2 X^2+X+2  0  X X^2+X X^2+2 X^2+X+2  2  0  0 X+2 X^2+2  X  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  2  X X+2  0 X^2+X X^2+X+2 X^2+2  0 X^2+X+2 X^2+X  X X^2+X X+2  X X^2+2 X^2+2 X^2+2  X X^2+X X^2  0 X+2  0  2 X^2+X  2 X^2 X+2  2  2 X^2 X^2+X X^2+X+2  0 X^2+X  X  X X^2+X X^2  X
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  2  0  2  0  2  0  0  2  2  0  2  0  0  2  2  2  0  2  2  2  0  2  0  2  2  0  2  2  2  0  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+136x^45+143x^46+270x^47+345x^48+422x^49+256x^50+176x^51+112x^52+96x^53+32x^54+34x^55+6x^56+18x^57+1x^78

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 0.141 seconds.