The generator matrix

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

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+232x^54+184x^55+683x^56+488x^57+855x^58+624x^59+877x^60+624x^61+916x^62+520x^63+715x^64+360x^65+448x^66+192x^67+240x^68+64x^69+98x^70+16x^71+33x^72+9x^74+11x^76+2x^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 3.91 seconds.