The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+145x^40+754x^41+1071x^42+2120x^43+2602x^44+4560x^45+4332x^46+6810x^47+6038x^48+8090x^49+6237x^50+7380x^51+4777x^52+4466x^53+2343x^54+1932x^55+850x^56+596x^57+208x^58+124x^59+49x^60+30x^61+17x^62+2x^63+2x^64

The gray image is a code over GF(2) with n=196, k=16 and d=80.
This code was found by Heurico 1.13 in 42.1 seconds.