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

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

Homogenous weight enumerator: w(x)=1x^0+136x^45+167x^46+254x^47+297x^48+438x^49+288x^50+192x^51+96x^52+80x^53+40x^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 0.14 seconds.