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  1  X  0  X  1  1  X  2  X  1  0  0  0  1  1  X  0  1  X  2  1  2  0
 0  X  0  0  0  0  0  0  0  X X+2  X  2 X+2  2  X  X  X  0 X+2  X X+2 X+2  X  0  2 X+2  X  2  2  X X+2  0  2 X+2  X  0  0  X  X  2  0  X  X  0  X  2  X  X  2  0
 0  0  X  0  0  0  X X+2  X  X  X  0  0 X+2  2  2  2  2  X X+2  X  0  X  X X+2  2  2  0  0 X+2  2  2  X X+2  X X+2  X X+2 X+2  X  X  2 X+2  2  X  X X+2 X+2  0  0  0
 0  0  0  X  0  X  X  X  2  0  0  2  2 X+2  0  X  2 X+2  X X+2  X  X  2 X+2  0 X+2 X+2  0  X  X  0  2 X+2  2  0  X X+2  0  X X+2  2  2  2 X+2  2  2 X+2  0  0  X  2
 0  0  0  0  X  X  2 X+2 X+2  0  X  X  0  0  X  X X+2  0  2  X  0  X  X X+2  0 X+2  2  2  0  0  2  0 X+2  X  X X+2  2  X  X  2  X  X  2 X+2  0 X+2  2  0  X X+2  2
 0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  2  2  2  0  2  0  0  0  2  0  2  0  0  0  0  2  0  2  0  0  0  0  2  2  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+317x^44+240x^46+904x^48+562x^50+924x^52+458x^54+415x^56+118x^58+111x^60+30x^62+15x^64+1x^72

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 16.1 seconds.