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

generates a code of length 49 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+145x^40+4x^41+384x^42+32x^43+591x^44+196x^45+770x^46+520x^47+1179x^48+556x^49+1226x^50+496x^51+820x^52+204x^53+492x^54+40x^55+346x^56+116x^58+53x^60+18x^62+2x^66+1x^72

The gray image is a code over GF(2) with n=196, k=13 and d=80.
This code was found by Heurico 1.16 in 3.85 seconds.