The generator matrix

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

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+368x^70+698x^72+845x^74+725x^76+595x^78+317x^80+261x^82+141x^84+89x^86+35x^88+18x^90+2x^92+1x^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 9.14 seconds.