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

generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+35x^40+26x^41+105x^42+120x^43+226x^44+200x^45+474x^46+228x^47+904x^48+284x^49+1366x^50+328x^51+1342x^52+296x^53+868x^54+240x^55+455x^56+186x^57+209x^58+96x^59+82x^60+32x^61+38x^62+12x^63+21x^64+8x^66+6x^68+4x^70

The gray image is a code over GF(2) with n=204, k=13 and d=80.
This code was found by Heurico 1.16 in 4.12 seconds.