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

generates a code of length 48 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+68x^39+130x^40+216x^41+243x^42+242x^43+373x^44+548x^45+763x^46+976x^47+1055x^48+976x^49+839x^50+558x^51+373x^52+284x^53+167x^54+122x^55+97x^56+80x^57+34x^58+16x^59+18x^60+8x^61+2x^62+2x^63+1x^80

The gray image is a code over GF(2) with n=192, k=13 and d=78.
This code was found by Heurico 1.16 in 3.71 seconds.