The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+238x^41+565x^42+1164x^43+1539x^44+2208x^45+2424x^46+3222x^47+3112x^48+3720x^49+3166x^50+3402x^51+2683x^52+2130x^53+1280x^54+952x^55+449x^56+310x^57+117x^58+54x^59+22x^60+2x^61+6x^63+2x^64

The gray image is a code over GF(2) with n=196, k=15 and d=82.
This code was found by Heurico 1.13 in 11.2 seconds.