The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+100x^54+112x^55+201x^56+112x^57+140x^58+88x^59+98x^60+20x^61+52x^62+36x^63+8x^64+12x^65+16x^66+4x^67+9x^68+12x^70+2x^72+1x^76

The gray image is a code over GF(2) with n=232, k=10 and d=108.
This code was found by Heurico 1.11 in 0.0903 seconds.