The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+103x^44+316x^45+486x^46+560x^47+669x^48+772x^49+822x^50+860x^51+814x^52+788x^53+694x^54+464x^55+314x^56+252x^57+122x^58+60x^59+43x^60+16x^61+20x^62+8x^63+8x^64

The gray image is a code over GF(2) with n=204, k=13 and d=88.
This code was found by Heurico 1.16 in 2.33 seconds.