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  X  0  1  0  X  1  1  0  1  X  2  1  1  1  2  2  0  1  2  X  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2 X+2  0  2  X  2 X+2 X+2  0  0 X+2  X  X  0  2  2  X X+2  X  2  0  0  0  X  X  2  0  X  X
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2 X+2 X+2  0  2 X+2  0  2  2  0 X+2 X+2  2  0  X  X X+2  0  X  2  2  2  0  X  2 X+2  X  X  X
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X X+2  2  X  0  X X+2  0  X  X  X  X  X  X X+2  2  2  0  0 X+2  X  2  X  X  X  2 X+2  2  X
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  0  0  2  0  2  0  2  2  2  0  2  2  2  2  0  2  2  0  0  2
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  0  0  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  0  0  0  0  2  0  0  2  0  2  0  0  0  0  2  2  2  2  2  0  0  2  2  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+347x^44+36x^45+204x^47+594x^48+484x^49+620x^51+508x^52+460x^53+196x^55+436x^56+44x^57+4x^59+136x^60+25x^64+1x^76

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 43.7 seconds.