The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  2  1  0  1  1  1  1  X X+2  1  1  X  X  X  1 X+2  2  1  1  1  X X+2 X+2  1  1  1  1  1  1  1  0 X+2  1  1  1  2  1  1  X  1  0  2  1  1  0  1
 0  1  0  0  1  1  1  2  0  0  1  1  1  1  1  X  3  2 X+3  1  1 X+3  X  1  2  1 X+3  1  X  0 X+1 X+2  1  1  X  1  2  3 X+3  1  X X+1  1  X X+1  2  X  1  2  X  0  1  1  1 X+1  1  1  0
 0  0  1  1  2  3  1  1  0  1  2  2  3  3  1 X+3 X+3 X+2 X+2 X+3  0  0  3  0  1  1 X+1 X+2  1  X  2  1  1  X  1 X+1 X+3 X+2  X X+3  2  3 X+1  1  1 X+1  X X+2  2  0  1  3  X  X  2 X+2  X  2
 0  0  0  X  0  X  X  X X+2  2  X X+2  0  2 X+2  X  2  0 X+2  2 X+2  2  0  0  0 X+2  X  X  X X+2  X  X  2  0  2  X X+2 X+2  2  0  2  2  X X+2 X+2  0 X+2  X  2  X  X  0  0 X+2  0  2  2 X+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+84x^53+219x^54+250x^55+274x^56+254x^57+208x^58+198x^59+113x^60+100x^61+81x^62+74x^63+67x^64+40x^65+50x^66+6x^67+5x^68+12x^69+2x^70+4x^72+6x^73

The gray image is a code over GF(2) with n=232, k=11 and d=106.
This code was found by Heurico 1.11 in 0.137 seconds.