The generator matrix

 1  0  0  0  0  1  1  1  0  1  2  1 X+2  0  X  1 X+2  1 X+2  0  1  2  1  1  X X+2  1  1  1  1  1  X  1  0 X+2  1 X+2  2 X+2  1 X+2  1 X+2  1  1  1  2  1  2  1  1
 0  1  0  0  0  0 X+1  X  0 X+3  1  X  1  1 X+2  3  1 X+3  1 X+2  1  2  0  X  1  1 X+2  0  3  X  1 X+2  1  X  1  X  1  1  0 X+2  2 X+2  1 X+3  1  0  1  2  1  2  0
 0  0  1  0  0  0  1 X+1  1  1  2  3 X+3  1  2  2 X+2 X+3  1  1  X  1  3  3  1  X  0 X+2 X+3 X+3  2  2 X+2  1 X+2  0 X+1  2  2  0  X  1  2  1  X  3  2 X+3 X+1  2  0
 0  0  0  1  0  1  2  3  3 X+1  1 X+2 X+1 X+3  1  0 X+3 X+2  X  3  3  X  2 X+3  2  0 X+1  0  X  1 X+2  1 X+3  X X+1 X+2  2 X+1 X+2  1  1  0 X+3  0  1  1  3  0  1  2  0
 0  0  0  0  1  1  3 X+2 X+3  3  X  3  2  3 X+3 X+1  3  2 X+1  2  X  3  2 X+3  X  3  0 X+3 X+3 X+3  1  2 X+3 X+3 X+3 X+2  0  3  1 X+2 X+1  0  X  2  1  1 X+3 X+3  2  2  0
 0  0  0  0  0  X  0  X  X X+2  X  2 X+2 X+2  X X+2  2 X+2  0  0  2  X  2  X X+2  X  2  2  X  0  0 X+2  0  2  X X+2  2  0 X+2  2  X  2  0  X  0  2  X  2  0  2  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+96x^40+208x^41+914x^42+1320x^43+2730x^44+3556x^45+5968x^46+6932x^47+10432x^48+11528x^49+14574x^50+13764x^51+14712x^52+12228x^53+10730x^54+7452x^55+5928x^56+3020x^57+2476x^58+1060x^59+806x^60+296x^61+214x^62+64x^63+47x^64+12x^65+4x^66

The gray image is a code over GF(2) with n=204, k=17 and d=80.
This code was found by Heurico 1.13 in 160 seconds.