The generator matrix

 1  0  0  0  0  1  1  1  0  1  2  1 X+2  0  X  X  1  1  1  2 X+2  1  1  1  0  1 X+2  1  1  1  1  X  1  1  2 X+2  X  1  2 X+2 X+2  1  1  2  1  1  0 X+2  1
 0  1  0  0  0  0 X+1  X  0 X+3  1  X  1  1 X+2  1  3  2  1  X  1 X+1  X  1  1  0  1 X+3  0 X+1  1  X  X  1  1  X  1 X+3  2  1  1  0 X+3  X  X X+2  1  1  2
 0  0  1  0  0  0  1 X+1  1  1  2  3 X+3  1  2  3  X  1 X+1  1  3  0  X  X  0 X+2 X+2  3 X+1  0  2  1 X+1  3  3  1  2 X+2  0  3  0 X+1  3  1  X  2 X+2 X+2  2
 0  0  0  1  0  1  2  3  3 X+1  1 X+2 X+1 X+3  1  2  0 X+2  2 X+2 X+2  2  0 X+1  3  1 X+2  1  3  1  0  3  0  2 X+1 X+2 X+3  3  1  2  0 X+1 X+1 X+2 X+1  3 X+3 X+3 X+2
 0  0  0  0  1  1  3 X+2 X+3  3  X  3  2  3 X+3  3 X+3 X+2  X X+3  0  2  1  0 X+1  X  1  0 X+3 X+1  3 X+2 X+2 X+1  X  2  0 X+2  X  3  0 X+1  0 X+3 X+1 X+3  1  1  0
 0  0  0  0  0  X  0  X  X X+2  X  2 X+2 X+2  X  0  0  2  0  2  0  2  2  X X+2 X+2  X  2  0  0 X+2  2 X+2  X  0  X  0  2 X+2  X X+2  X  0 X+2  0  0  X  2 X+2

generates a code of length 49 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+142x^39+606x^40+1166x^41+2364x^42+3638x^43+5760x^44+7238x^45+10280x^46+12474x^47+14307x^48+14288x^49+15192x^50+12200x^51+10844x^52+7612x^53+5496x^54+3450x^55+2080x^56+1002x^57+508x^58+218x^59+124x^60+54x^61+16x^62+6x^63+6x^64

The gray image is a code over GF(2) with n=196, k=17 and d=78.
This code was found by Heurico 1.13 in 152 seconds.