The generator matrix

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

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+114x^44+124x^46+80x^47+152x^48+96x^49+166x^50+80x^51+110x^52+58x^54+37x^56+2x^58+2x^62+1x^64+1x^88

The gray image is a code over GF(2) with n=196, k=10 and d=88.
This code was found by Heurico 1.16 in 1.6 seconds.