The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+91x^76+456x^77+659x^78+820x^79+922x^80+1106x^81+1223x^82+1322x^83+1316x^84+1036x^85+1344x^86+1200x^87+1050x^88+1046x^89+775x^90+638x^91+471x^92+360x^93+218x^94+132x^95+71x^96+48x^97+34x^98+12x^99+14x^100+8x^101+3x^102+4x^103+4x^105

The gray image is a code over GF(2) with n=340, k=14 and d=152.
This code was found by Heurico 1.16 in 15.7 seconds.