The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1 X+2  0  1  2  1  1  1  X  2  1  1  1  1  X  1  1  0  X  0  1 X+2  1  1 X+2  1  1  2  2  1  X  X  X  0  1  1  2  1  0  0  1  1  1  0  2  1  0 X+2 X+2  1  2  1  1 X+2  X  1  X  0  1  1 X+2  2  X  1  1  0
 0  1  0  0  1 X+1  1  0 X+2  2  3  1  1 X+3  2  0  2  1  1  1 X+1  X  3 X+1  1  X X+1  1  X  1  1  1 X+3 X+2  0  2  2  1  1  2  1  1 X+2  2  0  3  1  3  1  1  0  X  1  1  1 X+2  1  1  1 X+2  X  0  2  1  1  X  1  0 X+2  3  1  X X+2 X+1 X+2  X
 0  0  1  1  1  2  3  1  3  X X+2  X X+1  3  1  2  1  3 X+2 X+3  0  1  1  1  3  2  X X+2  1 X+2  0 X+1 X+3 X+3  1  2  2 X+1 X+1 X+2  0  1  1  1 X+3  0  0  X X+2  1  X  3  0  1  3 X+1 X+3  1 X+1  2  1 X+2 X+1 X+2 X+1  X X+1  1 X+3 X+3 X+2  1  1 X+1 X+2  1
 0  0  0  X X+2  0 X+2 X+2 X+2  0  0  0 X+2  X  X X+2  0  2 X+2  2  X  0  X X+2  0  X X+2  X  2  0  2 X+2  2  X  2 X+2  2 X+2  0  X  X  0 X+2  0 X+2  2  X  0  0 X+2  2  0 X+2  2  0  2  X X+2  2 X+2  X  0  X  2  X  X  0  2  0 X+2  0  2  X  2  X  X
 0  0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  2  2  2  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  2  0  2  2  0  0  0  0  0  2  0  0  2  0  2  2  0  0  2  2  0  2  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+346x^70+737x^72+843x^74+722x^76+552x^78+340x^80+274x^82+157x^84+72x^86+24x^88+23x^90+1x^92+2x^94+2x^96

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 28.6 seconds.