The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1 X+2  1  2  X  X  2  1  0  1  2  1  1  X  1  1  1  1  1  X  1  2  X  1  1  0  1 X+2  1  1  1  1  1  X  X X+2  X X+2  1  1
 0  1  0  0  0  2  1  3  1 X+2  0 X+1  1  1  1  1  1  2  0  0 X+2 X+2 X+3  3 X+2  0  X X+3 X+3 X+2  1 X+1  X  1 X+3 X+2  1  X  1  1  1  1 X+1 X+1  0  2  1  1  X X+1  2
 0  0  1  0  0  3  1  2  3  1  1  3  X X+2  1  X  2  1 X+3  1  1  0 X+2 X+3  1  X X+1 X+1  X  2 X+3  2  X  0  2 X+3  3 X+3  3  1 X+1 X+1  0  2  1  1 X+3 X+1  1  X  0
 0  0  0  1  1  1  2  3  3  0 X+3  3 X+3 X+2  X  1  0  X  3  1 X+2  1  0 X+3 X+3  1 X+1 X+2  3 X+2  1 X+3  1 X+3  2  3  1  0 X+2 X+3 X+2  0  1  1  X  3  2  3 X+2  1 X+2
 0  0  0  0  X  0  0  0  0 X+2  X  X  X X+2 X+2  X  2  2  2 X+2  X  2  2  X  2  0 X+2  2 X+2 X+2  0  0  0  0  X  0 X+2  2  2  X  0  X  0 X+2 X+2  2 X+2  2  X  X  0

generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+82x^43+320x^44+528x^45+838x^46+1128x^47+1347x^48+1594x^49+1588x^50+1642x^51+1688x^52+1594x^53+1307x^54+968x^55+724x^56+424x^57+288x^58+208x^59+76x^60+18x^61+10x^62+4x^63+4x^64+2x^65+1x^70

The gray image is a code over GF(2) with n=204, k=14 and d=86.
This code was found by Heurico 1.16 in 8.34 seconds.