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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+61x^50+100x^51+128x^52+228x^53+279x^54+354x^55+434x^56+544x^57+740x^58+862x^59+835x^60+850x^61+762x^62+524x^63+438x^64+304x^65+194x^66+174x^67+117x^68+104x^69+66x^70+24x^71+27x^72+16x^73+9x^74+8x^75+4x^76+2x^77+2x^79+1x^94

The gray image is a code over GF(2) with n=240, k=13 and d=100.
This code was found by Heurico 1.16 in 5.03 seconds.