The generator matrix

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

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+48x^44+156x^45+159x^46+372x^47+281x^48+518x^49+304x^50+518x^51+332x^52+516x^53+224x^54+302x^55+81x^56+136x^57+61x^58+18x^59+23x^60+16x^61+12x^62+6x^63+1x^64+2x^65+7x^66+1x^68+1x^70

The gray image is a code over GF(2) with n=204, k=12 and d=88.
This code was found by Heurico 1.16 in 0.688 seconds.