The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+77x^74+136x^75+212x^76+344x^77+472x^78+650x^79+838x^80+1034x^81+1206x^82+1304x^83+1377x^84+1376x^85+1294x^86+1244x^87+1215x^88+984x^89+815x^90+638x^91+335x^92+308x^93+156x^94+86x^95+89x^96+46x^97+51x^98+32x^99+25x^100+4x^101+20x^102+4x^103+1x^104+2x^106+2x^107+3x^108+2x^110+1x^114

The gray image is a code over GF(2) with n=340, k=14 and d=148.
This code was found by Heurico 1.16 in 22 seconds.