The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+273x^78+553x^80+672x^82+665x^84+565x^86+611x^88+449x^90+187x^92+44x^94+18x^96+31x^98+8x^100+10x^102+3x^104+4x^106+1x^112+1x^120

The gray image is a code over GF(2) with n=340, k=12 and d=156.
This code was found by Heurico 1.16 in 5.45 seconds.