The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+78x^53+75x^54+134x^55+96x^56+124x^57+74x^58+124x^59+66x^60+96x^61+39x^62+56x^63+26x^64+20x^65+1x^66+4x^67+1x^68+2x^69+2x^70+2x^71+1x^72+1x^74+1x^92

The gray image is a code over GF(2) with n=232, k=10 and d=106.
This code was found by Heurico 1.16 in 0.41 seconds.