The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+36x^76+38x^77+131x^78+90x^79+247x^80+308x^81+384x^82+696x^83+618x^84+1270x^85+781x^86+1750x^87+924x^88+1976x^89+926x^90+1728x^91+792x^92+1202x^93+564x^94+742x^95+337x^96+308x^97+197x^98+104x^99+79x^100+18x^101+43x^102+10x^103+21x^104+24x^106+10x^108+15x^110+5x^112+5x^114+1x^116+2x^118+1x^120

The gray image is a code over GF(2) with n=356, k=14 and d=152.
This code was found by Heurico 1.16 in 23.6 seconds.