The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+136x^53+351x^54+456x^55+707x^56+734x^57+865x^58+652x^59+797x^60+676x^61+641x^62+618x^63+530x^64+326x^65+259x^66+148x^67+143x^68+80x^69+40x^70+10x^71+14x^72+4x^74+4x^75

The gray image is a code over GF(2) with n=240, k=13 and d=106.
This code was found by Heurico 1.13 in 1.1 seconds.