The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+184x^40+96x^42+16x^43+490x^44+112x^45+648x^46+336x^47+1118x^48+560x^49+1096x^50+560x^51+1140x^52+336x^53+600x^54+112x^55+484x^56+16x^57+120x^58+122x^60+37x^64+8x^68

The gray image is a code over GF(2) with n=200, k=13 and d=80.
This code was found by Heurico 1.16 in 7.05 seconds.