The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+135x^50+390x^51+647x^52+976x^53+991x^54+1380x^55+1404x^56+1696x^57+1497x^58+1618x^59+1235x^60+1366x^61+1022x^62+762x^63+453x^64+388x^65+248x^66+112x^67+30x^68+6x^69+9x^70+10x^71+4x^72+2x^74+2x^76

The gray image is a code over GF(2) with n=232, k=14 and d=100.
This code was found by Heurico 1.13 in 3.81 seconds.