The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+64x^55+100x^56+128x^57+64x^58+80x^60+64x^63+9x^64+2x^80

The gray image is a code over GF(2) with n=232, k=9 and d=110.
This code was found by Heurico 1.16 in 17.2 seconds.