The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+172x^70+302x^71+457x^72+418x^73+423x^74+402x^75+348x^76+286x^77+249x^78+202x^79+201x^80+104x^81+183x^82+102x^83+69x^84+62x^85+35x^86+32x^87+31x^88+10x^89+2x^90+5x^92

The gray image is a code over GF(2) with n=304, k=12 and d=140.
This code was found by Heurico 1.16 in 0.871 seconds.