The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+254x^54+120x^55+760x^56+360x^57+1133x^58+380x^59+1036x^60+368x^61+1094x^62+388x^63+823x^64+264x^65+672x^66+132x^67+216x^68+32x^69+88x^70+4x^71+32x^72+19x^74+12x^76+4x^78

The gray image is a code over GF(2) with n=244, k=13 and d=108.
This code was found by Heurico 1.16 in 65.3 seconds.