The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+228x^60+444x^61+541x^62+590x^63+593x^64+756x^65+800x^66+764x^67+651x^68+580x^69+545x^70+470x^71+394x^72+304x^73+240x^74+128x^75+77x^76+40x^77+16x^78+16x^79+6x^80+4x^81+2x^82+2x^84

The gray image is a code over GF(2) with n=268, k=13 and d=120.
This code was found by Heurico 1.16 in 2.96 seconds.