The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  X  1  2  1  1  1 X+2  X  1  0  X  1  X  1  1  1 X+2  1  2  2  1  1  2  1  1  1 X+2  2  1  2  1  1  1  1  1  0 X+2  0  X  1  1  2 X+2  X  2  0  1
 0  1  0  0  3 X+1  1  2  0  0 X+3  1  1  1  3  X X+2  1  1  3 X+2  1  2  X X+3 X+1 X+2  2 X+1  1  1  0  3  0 X+1 X+2  X  1  1 X+2  1  0  1  3  2  X  1  X  1  1  1  0  X X+2  1  1  X  X
 0  0  1  1  3  2  3  1  2 X+1 X+3  2  2  1  1 X+2  3  2  3  1  1 X+1  X  1  0  1  3  1  X  2 X+3 X+2 X+3  1  X X+3  2 X+3  3  3 X+2  3 X+3  X X+1  0 X+2  1  2  X  0 X+3  1  1 X+1 X+3  1 X+2
 0  0  0  X  X  0  X  X X+2  2  0 X+2  X  2 X+2  0  0  2  2  0  2  X X+2  X  X X+2 X+2  2  2 X+2  2  2  2 X+2  X  X  0  0  X  2  0  0  X  0  X  X  X  2  2 X+2  0  0 X+2  0 X+2 X+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+90x^53+236x^54+198x^55+303x^56+248x^57+245x^58+126x^59+157x^60+108x^61+77x^62+58x^63+70x^64+54x^65+43x^66+2x^67+11x^68+6x^69+7x^70+2x^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 1.16 in 0.219 seconds.