The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+172x^55+168x^56+256x^57+211x^58+304x^59+133x^60+206x^61+93x^62+138x^63+64x^64+116x^65+56x^66+52x^67+31x^68+22x^69+6x^70+6x^71+3x^72+8x^73+1x^74+1x^78

The gray image is a code over GF(2) with n=240, k=11 and d=110.
This code was found by Heurico 1.16 in 0.246 seconds.