The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+280x^44+312x^46+513x^48+340x^50+386x^52+112x^54+80x^56+4x^58+14x^60+6x^64

The gray image is a code over GF(2) with n=196, k=11 and d=88.
This code was found by Heurico 1.16 in 0.614 seconds.