The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+43x^80+68x^81+90x^82+118x^83+148x^84+126x^85+143x^86+222x^87+222x^88+232x^89+167x^90+102x^91+76x^92+72x^93+52x^94+38x^95+31x^96+20x^97+23x^98+14x^99+20x^100+10x^101+2x^102+1x^104+2x^106+2x^107+2x^108+1x^150

The gray image is a code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.777 seconds.