The generator matrix

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

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+178x^62+84x^63+390x^64+136x^65+485x^66+188x^67+524x^68+224x^69+550x^70+172x^71+462x^72+136x^73+254x^74+68x^75+122x^76+16x^77+54x^78+23x^80+13x^82+8x^84+2x^86+4x^88+2x^92

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 34.9 seconds.