The generator matrix

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

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+149x^54+290x^55+427x^56+368x^57+423x^58+370x^59+361x^60+360x^61+325x^62+240x^63+221x^64+152x^65+141x^66+98x^67+93x^68+32x^69+22x^70+10x^71+9x^72+4x^74

The gray image is a code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.11 in 0.317 seconds.