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

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+41x^52+104x^53+100x^54+154x^55+158x^56+192x^57+246x^58+212x^59+217x^60+148x^61+125x^62+96x^63+64x^64+56x^65+32x^66+30x^67+25x^68+20x^69+9x^70+2x^71+3x^72+8x^73+2x^75+2x^76+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 0.337 seconds.