The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  1  0  1  0  1  1  2  1  1  X  1  1  1 X+2  1  1  X  1  1  1  2  1  1 X+2  1  1  1  2 X+2  0  1  1  X  X  1  1
 0  1  1  0  1  1  2 X+1  1  0  1 X+1  1  2  1 X+3  1  X X+1  1  3 X+2  1  X  0 X+3  1 X+2 X+1  1 X+2 X+2 X+1  1 X+2 X+1  1  3 X+1  0  1  1  X X+3  2  1  1 X+1  0
 0  0  X  0  0  0  0  0  0  0  0  2  2 X+2 X+2  X  X  X  X  X  X X+2 X+2  2  2  2  2  0  2  0  X X+2  2 X+2  2 X+2  2  2  2 X+2  2 X+2  X  0  2 X+2  X  2  0
 0  0  0  X  0  0  0  0  X X+2 X+2 X+2 X+2 X+2  0  X X+2  2  2 X+2  X  X  2  2 X+2  0  2  X  2  2  0  X  X  0 X+2  2 X+2  X X+2  2  2 X+2  X  2  0  2 X+2  2 X+2
 0  0  0  0  X  0  2 X+2  0  2  2  X X+2  X  X  2  X X+2  0  X  2 X+2  X  0  0  0  X X+2  0  X  0  2  2  2  X X+2 X+2  0 X+2  2  X  0  0 X+2 X+2 X+2  2  2  0
 0  0  0  0  0  X X+2 X+2 X+2 X+2  0  0  X  0  0  X  X X+2  X  2  2 X+2  X  X X+2 X+2  X  2  2  0  2  0  2  0 X+2 X+2 X+2  X X+2  X  0  2  X  X  X  X X+2  0 X+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+120x^40+44x^41+496x^42+180x^43+880x^44+684x^45+1540x^46+1372x^47+2104x^48+1648x^49+2138x^50+1280x^51+1572x^52+668x^53+782x^54+236x^55+368x^56+28x^57+150x^58+4x^59+68x^60+14x^62+7x^64

The gray image is a code over GF(2) with n=196, k=14 and d=80.
This code was found by Heurico 1.16 in 10.1 seconds.