The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+124x^62+116x^63+386x^64+232x^65+422x^66+236x^67+439x^68+368x^69+398x^70+236x^71+332x^72+232x^73+274x^74+116x^75+82x^76+36x^78+21x^80+20x^82+14x^84+6x^86+3x^88+1x^92+1x^96

The gray image is a code over GF(2) with n=276, k=12 and d=124.
This code was found by Heurico 1.16 in 1.03 seconds.