The generator matrix

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

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+252x^43+720x^44+1226x^45+1482x^46+2176x^47+2394x^48+3218x^49+3004x^50+3612x^51+3181x^52+3420x^53+2518x^54+2160x^55+1427x^56+960x^57+488x^58+304x^59+107x^60+66x^61+28x^62+8x^63+10x^64+6x^65

The gray image is a code over GF(2) with n=204, k=15 and d=86.
This code was found by Heurico 1.13 in 11.8 seconds.