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  1  1  1  0  1  X  1  1  1  X  1  1  1  1  2  1  1  X  X  1  1  0  2  1  X  0  1  1  X  1  X  1  X
 0  X  0  0  0  X X+2  X  2  2  X  0  0  X  X X+2  0  0 X+2  X  2  X X+2  X  2  0  2  2 X+2  0  X X+2  X X+2 X+2  X  0  X  2 X+2  2  2  X  X X+2 X+2 X+2  2  0  2  X  0 X+2  X X+2  0  0 X+2 X+2  X  2  X  0  0 X+2  0  2
 0  0  X  0  X  X  X  0  2  0 X+2  X X+2  0 X+2  0  2 X+2  2 X+2  0  2  X  0 X+2 X+2  X  2  X  2  0 X+2  X  X  0  2  0  2 X+2  2 X+2 X+2  2  2  2 X+2  2  0  X  0 X+2 X+2  2  0  X  X  X  0  0  X  0  2  0  X  0  0  0
 0  0  0  X  X  0  X X+2  0  X  2  X  2 X+2  X  0  2  X  X  0 X+2  2 X+2 X+2  0  0 X+2  X  X  0  0  0  0  0  2  2  2  2 X+2  2  X  0 X+2  X  X  0  2 X+2  X  2  X  0  X  2 X+2  0 X+2  2  2 X+2  X  0  X  0  0 X+2  X
 0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  2  2  0  0  0  2  0  2  2  2  2  0  0  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0  2  0  2  0  2  2  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  2
 0  0  0  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  0  2  2  2  2  0  2  0  2  0  2  2  2  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  0  2  2  0  2  2  2  2  0  0  2  0  0  2  0  0  0  2  0  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+126x^60+12x^61+160x^62+40x^63+281x^64+116x^65+276x^66+176x^67+229x^68+116x^69+176x^70+40x^71+124x^72+12x^73+72x^74+51x^76+16x^78+18x^80+4x^82+1x^84+1x^108

The gray image is a code over GF(2) with n=268, k=11 and d=120.
This code was found by Heurico 1.16 in 0.567 seconds.