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

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+235x^44+128x^46+356x^48+128x^50+122x^52+42x^56+11x^60+1x^80

The gray image is a code over GF(2) with n=192, k=10 and d=88.
This code was found by Heurico 1.16 in 92.4 seconds.