The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  0  0  1  1  X  1  0  X  0  1  1  0  X  X
 0  X  0  X  0  0  X X+2  0  2  X X+2  0 X+2  2 X+2  2  2  X X+2  2 X+2 X+2  2  2 X+2  2 X+2  X  X X+2  X  2  2  0  2  2  X  X X+2 X+2 X+2  0  X  0  0 X+2  0  2 X+2  2
 0  0  X  X  0 X+2  X  0  2  X  X  0  2 X+2  X  0 X+2  2  X  X  0  0  0 X+2  0  X  2 X+2  X  2  2 X+2  X  X  X X+2 X+2  0  2  0  2  0  X  2 X+2  X X+2  2  X  0  2
 0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  0  2  0  2  2  0  2  0  2  2  2  0  2  2  2  0  0  2  2  2  2  2  2  2  2  0  2  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  2  0  0  2  0  0  0  2  2  0  2  2  2  0  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  0  2  0  0  2  2  0  0  0  0  2  0  2  2  0  0  2  0  0  2  0  0  2  2  0  2  0  0  0  2  0  2  2
 0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  2  2  2  0  0  2  2  2  2  2  0  2  2  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  2  0  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+103x^44+8x^45+146x^46+48x^47+253x^48+120x^49+286x^50+160x^51+315x^52+120x^53+182x^54+48x^55+116x^56+8x^57+82x^58+37x^60+8x^62+5x^64+1x^68+1x^80

The gray image is a code over GF(2) with n=204, k=11 and d=88.
This code was found by Heurico 1.16 in 0.296 seconds.