The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+178x^69+326x^70+426x^71+400x^72+456x^73+353x^74+336x^75+288x^76+298x^77+227x^78+172x^79+147x^80+144x^81+83x^82+88x^83+53x^84+56x^85+27x^86+18x^87+14x^88+4x^89+1x^92

The gray image is a code over GF(2) with n=300, k=12 and d=138.
This code was found by Heurico 1.11 in 0.483 seconds.