The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+134x^75+472x^76+858x^77+1212x^78+1526x^79+1800x^80+2056x^81+2259x^82+2288x^83+2537x^84+2674x^85+2586x^86+2618x^87+2216x^88+1886x^89+1580x^90+1256x^91+1022x^92+680x^93+502x^94+288x^95+135x^96+90x^97+49x^98+18x^99+9x^100+12x^101+4x^102

The gray image is a code over GF(2) with n=340, k=15 and d=150.
This code was found by Heurico 1.13 in 21.6 seconds.