The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+116x^53+286x^54+396x^55+457x^56+388x^57+410x^58+340x^59+296x^60+360x^61+274x^62+260x^63+160x^64+116x^65+94x^66+60x^67+43x^68+12x^69+24x^70+2x^72+1x^76

The gray image is a code over GF(2) with n=236, k=12 and d=106.
This code was found by Heurico 1.11 in 0.309 seconds.