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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1  X  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  0  2  2  0  2  2  0  0  2  0  2  0  2  0  0
 0  0  2  0  0  0  0  0  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  2  0  2  0  2  0  2  2  2  0  0  2  0  0  2  0  0  2  2  2  0  0  0
 0  0  0  2  0  0  0  0  2  0  0  2  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  0  2  0  2  2  2  2  0  2  0  0  0  0  0  2  0  2  2  0  2  0  0  2
 0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  2  0  0  0  2  2  0  2  2  2  2  0  0  2  2  0  0  2  0  0  2  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  0  2  2  0  0  0  2  0  2  2  0  0  2  0  0  2  2  0  2  2  2  0  0  0  0  2  2  0  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  2  0  0  0  2  2  0
 0  0  0  0  0  0  2  0  2  2  0  0  0  2  2  0  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  0  2  0  2  0  2  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  0  2
 0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  2  2  2  2  2  2  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+67x^60+91x^64+96x^66+512x^67+142x^68+32x^70+42x^72+31x^76+9x^80+1x^128

The gray image is a code over GF(2) with n=268, k=10 and d=120.
This code was found by Heurico 1.16 in 0.249 seconds.