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

generates a code of length 48 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+39x^44+106x^46+223x^48+100x^50+40x^52+2x^54+1x^92

The gray image is a code over GF(2) with n=192, k=9 and d=88.
This code was found by Heurico 1.16 in 0.0628 seconds.