The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+61x^44+6x^45+64x^46+70x^47+129x^48+168x^49+219x^50+296x^51+362x^52+484x^53+433x^54+484x^55+349x^56+296x^57+197x^58+168x^59+82x^60+70x^61+70x^62+6x^63+30x^64+30x^66+6x^68+9x^70+3x^72+1x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=216, k=12 and d=88.
This code was found by Heurico 1.16 in 1.15 seconds.