The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+49x^70+54x^71+156x^72+254x^73+292x^74+490x^75+610x^76+828x^77+1047x^78+1142x^79+1279x^80+1292x^81+1415x^82+1384x^83+1301x^84+1252x^85+957x^86+774x^87+611x^88+386x^89+229x^90+206x^91+104x^92+64x^93+78x^94+46x^95+20x^96+20x^97+21x^98+9x^100+4x^102+5x^104+3x^106+1x^110

The gray image is a code over GF(2) with n=328, k=14 and d=140.
This code was found by Heurico 1.16 in 20.4 seconds.