The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+144x^52+32x^53+122x^54+257x^56+224x^57+250x^58+296x^60+224x^61+190x^62+156x^64+32x^65+78x^66+20x^68+17x^72+3x^76+1x^80+1x^92

The gray image is a code over GF(2) with n=236, k=11 and d=104.
This code was found by Heurico 1.16 in 24.4 seconds.