The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+164x^62+381x^64+352x^66+290x^68+366x^70+321x^72+128x^74+22x^76+10x^78+7x^80+2x^86+1x^88+2x^94+1x^96

The gray image is a code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 95.9 seconds.