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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+83x^52+8x^53+205x^54+96x^55+267x^56+232x^57+275x^58+400x^59+256x^60+552x^61+218x^62+448x^63+229x^64+216x^65+217x^66+80x^67+134x^68+16x^69+87x^70+45x^72+19x^74+6x^76+2x^78+2x^80+1x^82+1x^84

The gray image is a code over GF(2) with n=244, k=12 and d=104.
This code was found by Heurico 1.16 in 1.26 seconds.