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

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+58x^39+140x^40+198x^41+298x^42+308x^43+459x^44+600x^45+738x^46+884x^47+875x^48+912x^49+744x^50+608x^51+440x^52+272x^53+201x^54+166x^55+120x^56+66x^57+62x^58+20x^59+13x^60+4x^62+4x^63+1x^70

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.