The generator matrix

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

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+450x^44+920x^46+833x^48+732x^50+584x^52+384x^54+134x^56+44x^58+14x^60

The gray image is a code over GF(2) with n=196, k=12 and d=88.
This code was found by Heurico 1.16 in 5.44 seconds.