The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+77x^54+208x^55+115x^56+240x^57+48x^58+344x^59+40x^60+256x^61+84x^62+320x^63+83x^64+144x^65+32x^66+24x^67+8x^68+11x^70+7x^72+2x^78+2x^80+2x^86

The gray image is a code over GF(2) with n=240, k=11 and d=108.
This code was found by Heurico 1.16 in 1.23 seconds.